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    Vector Algebra VITEEE Quiz 2027 - Practice Questions

    Vector Algebra VITEEE Quiz 2027 - Practice Questions

    Shivani PooniaUpdated on 27 Oct 2026, 05:16 PM IST

    Vector Algebra VITEEE Quiz 2027 - Vector Algebra forms an important part of the Maths syllabus for VITEEE. The questions from this chapter are asked on vectors, magnitude, direction cosines, dot products, cross products, scalar triple products, and vector equations. Continuous practice with the help of VITEEE Vector Algebra Important Questions can assist students in solving questions faster. Below is a VITEEE Vector Algebra Quiz that includes multiple-choice questions on the basis of important Vector Algebra concepts. In this article, we have provided VITEEE Vector Algebra questions, as it will help candidates to prepare for the VITEEE Exam. 

    This Story also Contains

    1. VITEEE Vector Algebra Quiz
    2. VITEEE Vector Algebra Important Topics 2027
    3. Important VITEEE Vector Algebra Formulas
    4. Preparation Tips for Vector Algebra in VITEEE
    5. Best Books for VITEEE Vector Questions
    6. Why Practice VITEEE Vector Algebra MCQs
    Vector Algebra VITEEE Quiz 2027 - Practice Questions
    Vector Algebra VITEEE Quiz 2027 - Practice Questions

    VITEEE Vector Algebra Quiz

    Questions in VITEEE Vector Algebra will help students practice important topics and check their readiness. Answer the questions given below in order to enhance your proficiency in Vector Algebra.

    Question 1. Find the unit vector perpendicular to the plane of $\hat{i}-\hat{j}+2 \hat{k}$ and $\hat{i}+3 \hat{k}$ 

    (1) $\frac{2 \hat{i}-\hat{j}+5 \hat{k}}{\sqrt{30}}$ 

    (2) $\frac{-3 \hat{i}-\hat{j}+\hat{k}}{\sqrt{11}}$ 

    (3) $\frac{-3 \hat{i}-\hat{j}+\hat{k}}{2}$ 

    (4) None of these. 

    Correct answer: 2

    Solution:

    Unit vector perpendicular to the plane of vector a and b - $
    \frac{\vec{a} \times \vec{b}}{|\vec{a} \times \vec{b}|}
    $

    Here $\vec{a}$ and $\vec{b}$ are two vectors.

    $
    \begin{aligned}
    & \vec{a} \times \vec{b}=\left|\begin{array}{ccc}
    \hat{i} & \hat{j} & \hat{k} \\
    1 & -1 & 2 \\
    1 & 0 & 3
    \end{array}\right|=-3 \hat{i}-\hat{j}+\hat{k} \\
    & \frac{\vec{a} \times \vec{b}}{|\vec{a}||\vec{b}|}=\frac{-3 \hat{i}-\hat{j}+\hat{k}}{\sqrt{11}}
    \end{aligned}
    $

    Hence, the correct answer is the option (2)

    Question 2. Find $(\vec{a} \times \vec{b})^2$ if $\vec{a} \cdot \vec{b}=2$ and $|\vec{a}|=5$ and $|\vec{b}|=\frac{1}{2}$ 

    (1) $\frac{9}{4}$ 

    (2) $\frac{1}{4}$ 

    (3) $-\frac{9}{4}$ 

    (4) $\frac{1}{2}$ 

    Correct answer: 1

    Solution:
    Lagrange's identity -

    $
    (\vec{a} \times \vec{b})=|\vec{a}|^2|\vec{b}|^2-(\vec{a} \cdot \vec{b})^2
    $

    - wherein

    Here $\vec{a}$ and $\vec{b}$ are two vectors

    $
    (\vec{a} \times \vec{b})^2=|\vec{a}|^2|\vec{b}|^2-(\vec{a} \cdot \vec{b})^2=\frac{25}{4}-4=\frac{9}{4}
    $

    Hence, the correct answer is option (1).

    Question 3. Find the scalar triple product $[\vec{a} \vec{b} \vec{c}]$, where

    $
    \vec{a}=\hat{i}-\hat{j}, \quad \vec{b}=2 \hat{i}-2 \hat{j}+\hat{k}, \quad \vec{c}=2 \hat{i}+\hat{j}-3 \hat{k} .
    $

    (1) -3

    (2) 2

    (3) 3

    (4) 7

    Correct answer: 1

    Solution:
    Scalar Triple Product -
    $
    \begin{aligned}
    & {[\vec{a} \vec{b} \vec{c}]} \\
    & =(\vec{a} \times \vec{b}) \cdot \vec{c}=\vec{a} \cdot(\vec{b} \times \vec{c}) \\
    & =(\vec{b} \times \vec{c}) \cdot \vec{a}=\vec{b} \cdot(\vec{c} \times \vec{a}) \\
    & =(\vec{c} \times \vec{a}) \cdot \vec{b}=\vec{c} \cdot(\vec{a} \times \vec{b})
    \end{aligned}
    $
    - wherein

    Scalar Triple Product of three vectors $\hat{a}, \hat{b}, \hat{c}$.

     $\begin{bmatrix} \vec{a} & \vec{b} & \vec{c} \end{bmatrix}=(\vec{a}\times \vec{b})\cdot \vec{c}=\begin{vmatrix} 2 & 1 &-3 \\ 1& -1 &0 \\ 2 & -2 & 1 \end{vmatrix}$

     $=-2-1+0=-3$

    Hence, the correct answer is -3.

    Question 4: If $3 \vec{a} \cdot(\vec{b} \times \vec{c})=17$, then $33\left[\begin{array}{lll}\vec{a} & \vec{b} & \vec{c}\end{array}\right]=$ 

    (1) 33

    (2) 51

    (3) 187

    (4) 561

    Correct answer: 3

    Solution:

    Properties of Scalar Triple Product -

    $
    [K \vec{a} \vec{b} \vec{c}]=K[\vec{a} \vec{b} \vec{c}]
    $

    wherein
    $\vec{a}, \vec{b}$ and $\vec{c}$ are the three vectors.

    $
    \begin{aligned}
    & 3 \vec{a} \cdot(\vec{b} \times \vec{c})=3\left[\begin{array}{lll}
    \vec{a} & \vec{b} & \vec{c}
    \end{array}\right]=17 \\
    & {\left[\begin{array}{lll}
    \vec{a} & \vec{b} & \vec{c}
    \end{array}\right]=\frac{17}{3}} \\
    & 33\left[\begin{array}{lll}
    \vec{a} & \vec{b} & \vec{c}
    \end{array}\right]=187
    \end{aligned}
    $

    Hence, the answer is the option 3.

    Question 5: $\begin{bmatrix} \vec{a}+\vec{b} &\vec{b}+\vec{c} &\vec{c}+\vec{a} \end{bmatrix}=$ 

    (1) $\begin{bmatrix} \vec{a} & \vec{b} & \vec{c} \end{bmatrix}$ 

    (2) $\begin{bmatrix} \vec{a} & \vec{b} & \vec{c} \end{bmatrix}^{2}$ 

    (3) $2\begin{bmatrix} \vec{a} & \vec{b} & \vec{c} \end{bmatrix}$ 

    (4) $3\begin{bmatrix} \vec{a} & \vec{b} & \vec{c} \end{bmatrix}$ 

    Correct answer: 3

    Solution:
    Properties of Scalar Triple Product -
    $
    \begin{bmatrix} \vec{a}+\vec{b} &\vec{b}+\vec{c} &\vec{c}+\vec{a} \end{bmatrix}=2[\vec{a} \vec{b} \vec{c}]
    $
    - wherein
    $\vec{a}, \vec{b}, \vec{c}$ are three vectors

    Hence, the correct answer is the option (3).

    Question 6. Find the scalar triple product of the vectors $\hat{i}-\hat{j}, 2 \hat{i}+3 \hat{j},-3 \hat{i}-\hat{j} .$ 

    (1) 0

    (2) 10

    (3) 9

    (4) 24

    Correct answer:1

    Solution:
    Coplanar vectors -
    $
    [\vec{a} \vec{b} \vec{c}]=0
    $
    - wherein
    $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors.
    Given that 3 vectors are coplanar ( $x-y$ plane)

    Hence, the correct answer is 0.

    Question 7: Find volume of parallelepiped having 3 co-terminal edges as $\hat{i}-\hat{j}, \hat{j}+2 \hat{k}, \hat{i}-3 \hat{j}+\hat{k}$. 

    (1) 5

    (2) 15
    (3) 16

    (4) 6

    Correct answer: 1

    Solution:

    The volume of a parallelepiped is:

    $
    V=[\vec{a} \vec{b} \vec{c}]
    $

    - wherein

    Sides are represented by $\vec{a}, \vec{b}, \vec{c}$

    $
    \left[\begin{array}{lll}
    \vec{a} & \vec{b} & \vec{c}
    \end{array}\right]=\left|\begin{array}{ccc}
    1 & -1 & 0 \\
    0 & 1 & 2 \\
    1 & -3 & 1
    \end{array}\right|=5
    $

    Hence, the correct answer is option (1).

    Question 8: If the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{3}$, whereas angle between $\vec{a} \times \vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$. Find the volume of parallelepiped formed by $\vec{a}, \vec{b}$ and $\vec{c}$ where

    $|\vec{a}|=|\vec{b}|=2 \text { and }|\vec{c}|=2 \sqrt{3}$ 

    (1) $2\sqrt3$ 

    (2) $6\sqrt3$ 

    (3) $8\sqrt3$ 

    (4) $4\sqrt3$ 

    Correct option: 2

    Solution:

    Volume of parallelepiped -

    $\vec{a}, \vec{b}$ and $\vec{c}$ are the three edges if Parallelepiped. Volume $=a b c \cos \alpha \sin \theta$
    $
    \text { Volume }=2 \times 2 \times 2 \sqrt{3} \times \sin \frac{\pi}{3} \times \cos \frac{\pi}{6}=6 \sqrt{3}
    $

    Hence, the answer is option (2).

     

    Question 9: Find volume of tetrahedron formed by vectors $\hat{i}-\hat{j}+2 \hat{k}, 2 \hat{i}+\hat{j}$ and $\hat{j}-2 \hat{k}$ is : 

    (1) $\frac{1}{8}$ 

    (2) $\frac{1}{3}$ 

    (3) $\frac{8}{3}$ 

    (4) $\frac{3}{8}$ 

    Correct option: 2

    Solution:
    Volume of tetrahedron -

    $
    \frac{1}{6}[\vec{a} \vec{b} \vec{c}]
    $

    - wherein

    The vertices of tetrahedron are $\vec{o}, \vec{a}, \vec{b}, \vec{c}$.

    $
    \mathrm{V}=\frac{1}{6}\left[\begin{array}{lll}
    \vec{a} & \vec{b} & \vec{c}
    \end{array}\right]=\frac{1}{6}| | \begin{array}{ccc}
    1 & -1 & 2 \\
    2 & 1 & 0 \\
    0 & 1 & -2
    \end{array}| |=\frac{1}{6}|(-2-4+4)|=\frac{1}{3}
    $

    Hence, the correct answer is option (2).

     

    Question 10: Find $(\vec{a})^{\prime},(\vec{b})^{\prime},(\vec{c})^{\prime}$ which are reciprocal system of vectors of $\hat{i}+\hat{j}-\hat{k}, \hat{j}+2 \hat{k}$ and $\hat{i}-\hat{j}$. 

    (1) $\frac{1}{5}\hat{i}+\frac{2}{5}\hat{j}-\frac{2}{5}\hat{k}\: ;\: \frac{1}{5}\hat{i}-\frac{1}{5}\hat{j}+\frac{1}{5}\hat{k}\: ;\: \frac{1}{5}\hat{i}-\frac{2}{5}\hat{j}+\frac{1}{5}\hat{k}$ 

    (2) $\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}+\frac{2}{3}\hat{k}\: ;\: \frac{2}{5}\hat{i}+\frac{2}{5}\hat{j}-\frac{1}{5}\hat{k}\: ;\: \frac{3}{5}\hat{i}-\frac{2}{5}\hat{j}+\frac{1}{5}\hat{k}$ 

    (3) $\frac{2}{5}\hat{i}+\frac{2}{5}\hat{j}-\frac{1}{5}\hat{k}\: ;\: \frac{1}{5}\hat{i}+\frac{1}{5}\hat{j}+\frac{2}{5}\hat{k}\: ;\: \frac{3}{5}\hat{i}-\frac{2}{5}\hat{j}+\frac{1}{5}\hat{k}$ 

    (4) None of these 

    Correct option: 3

    Solution:
    Reciprocal System of Vectors -

    $
    \begin{aligned}
    \vec{a}^{\prime} & =\frac{\vec{b} \times \vec{c}}{[\vec{a} \vec{b} \vec{c}]} \\
    \vec{b}^{\prime} & =\frac{\vec{c} \times \vec{a}}{[\vec{a} \vec{b} \vec{c}]} \\
    \vec{c}^{\prime} & =\frac{\vec{a} \times \vec{b}}{[\vec{a} \vec{b} \vec{c}]}
    \end{aligned}
    $

    - wherein
    $\vec{a}, \vec{b}, \vec{c}$ are three vectors.

    $\begin{aligned} & {\left[\begin{array}{lll}\vec{a} & \vec{b} & \vec{c}\end{array}\right]=\left|\begin{array}{ccc}1 & 1 & -1 \\ 0 & 1 & 2 \\ 1 & -1 & 0\end{array}\right|=2+2+1=5} \\ & \vec{b} \times \vec{c}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 0 & 1 & 2 \\ 1 & -1 & 0\end{array}\right|=2 \hat{i}+2 \hat{j}-\hat{k} \\ & \vec{c} \times \vec{a}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 1 & -1 & 0 \\ 1 & 1 & -1\end{array}\right|=\hat{i}+\hat{j}+2 \hat{k} \\ & \vec{a} \times \vec{b}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & -1 \\ 0 & 1 & 2\end{array}\right|=3 \hat{i}-2 \hat{j}+\hat{k}\end{aligned}$

    Hence, the correct answer is option (3).

     

    Question 11: Find vector area of $\triangle A B C$, if position vectors of vertices are $\hat{i}+\hat{j}, \hat{j}+\hat{k}, \hat{k}+\hat{i}$. 

    (1) $\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$ 

    (2) $\frac{1}{2}(\hat{i}+\hat{j})\times\hat{k}$ 

    (3) $\frac{1}{2}(\hat{i}+\hat{j}+\hat{k})$ 

    (4) $\frac{1}{2}(\hat{i}\times\hat{j}+\hat{j}\times\hat{k})$ 

    Correct option: 3

    Solution:

    Vector Area -
    area of $\triangle A B C$

    $
    =\frac{1}{2}[\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}]
    $

    - wherein
    $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors.
    Vector Area -
    area of $\triangle A B C$

    $
    =\frac{1}{2}[\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}]
    $

    - wherein
    $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors.

    $\begin{aligned} \ area \ of \ triangle \ A B C & =\frac{1}{2}[(\hat{i}+\hat{j}) \times(\hat{j}+\hat{k})+(\hat{j}+\hat{k}) \times(\hat{k}+\hat{i})+(\hat{k}+\hat{i}) \times(\hat{i}+\hat{j})] \\ & =\frac{1}{2}[(\hat{k}-\hat{j}+\hat{i})+(\hat{i}-\hat{k}+\hat{j})+(\hat{j}-\hat{i}+\hat{k})] \\ & =\frac{1}{2}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$

    Hence, the correct answer is option (3).

     

    Question 12: If $ A (0,1,3) , B (1,-1,2) , C (1,1,1) and D (0,2,1)$ are four vertices of a tetrahedron , then volume of ABCD is: 

    (1) $\frac{1}{3}$ 

    (2) $\frac{1}{2}$ 

    (3) 2

    (4) 7

    Correct option: 2

    Solution:

     $1=\frac{1}{6}\left ( A\vec{B} \times A\vec{C}\right )\cdot A\vec{D}=\frac{1}{6}1\begin{vmatrix} 1 &-2 &-1 \\ 1&0 &-2 \\ 0&1 &-2 \end{vmatrix}1=\frac{1}{6}\times 3=\frac{1}{2}$

    Hence, the answer is option (2).

     

    Question 13: What is moment of force, $\vec{F}=\hat{i}-2 \hat{j}+\hat{k}$ about O , where radius vector is $\vec{r}=2 \hat{i}+2 \hat{j}-3 \hat{k}$ ? 

    (1) $\frac{2}{5}\hat{i}-\frac{1}{5}\hat{j}+\frac{3}{5}\hat{k}$ 

    (2) $2\hat{i}+3\hat{j}+2\hat{k}$ 

    (3) $4\hat{i}+6\hat{j}+5\hat{k}$ 

    (4) $-4\hat{i}-5\hat{j}-6\hat{k}$ 

    Correct option: 4

    Solution:

    Applications of Vectors -

    $
    \vec{M}=\vec{r} \times \vec{F}
    $

    - wherein
    $\vec{r}$ is position vector of P part M is moment of $\vec{F}$ about O . Direction of $\vec{M}$ is along the normal to the plane OPN .

    $
    \vec{M}=\left|\begin{array}{ccc}
    \hat{i} & \hat{j} & \hat{k} \\
    2 & 2 & -3 \\
    1 & -2 & 1
    \end{array}\right|=-4 \hat{i}-5 \hat{j}-6 \hat{k}
    $
    Hence, the correct answer is Option (4).

     

    Question 14: What is work done by a force, $\vec{F}=2 \hat{i}-\hat{j}+3 \hat{k}$ when displacement is $\vec{d}=\hat{i}+\hat{k}_?$ 

    (1) 5

    (2) 3

    (3) 6

    (4) 10

    Correct option: 1

    Solution:

    $\hat{W}=\hat{c} \cdot \hat{a}=2-0+3=5$ units

    Hence, the correct answer is 5. 

    Question 15: $\vec{a} \times(\vec{b} \times \vec{c})$ is in plane of: 

    (1) $\vec{b}$ and $\vec{c}$ 

    (2) $\vec{a}$ and $\vec{b}$ 

    (3) $\vec{a}$ and $\vec{c}$ 

    (4) $\vec{a} \times \vec{b}$ and $\vec{c}$ 

    Correct option: 1

    Solution:

    For three vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ vector triple product is defined as $\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})$. $\vec{a} \times(\vec{b} \times \vec{c})=(\vec{a} \cdot \vec{c}) \cdot \vec{b}-(\vec{a} \cdot \vec{b}) \cdot \vec{c}$

    $\vec{a} \times(\vec{b} \times \vec{c})=x \vec{b}+y \vec{c}$

    x and y are scalars.

    Hence, the answer is the option 1.

     

    Question 16: $\hat{i}\times (2\hat{i}\times \hat{j})$  is along which axis : 

    (1) X-axis 

    (2) Y-axis 

    (3) Z-axis 

    (4) None of these 

    Correct option: 2 

    Solution

    Vector Triple Product -

    $\vec{a} \times(\vec{b} \times \vec{c})$ is a vector perpendicular to $\vec{a}$ and $(\vec{b} \times \vec{c})$ 

    Perpendicular to $\hat{i}$ and $2 \hat{i} \times \hat{j}$, $\hat{i}$ and $\hat{k} \rightarrow \hat{j}($ or $Y-$ axis $)$

    Hence, the correct answer is option (2).

     

    Question 17: $\vec{a} \times(\vec{b} \times \vec{c})$ is called : 

    (1) Vector product 

    (2) Vector triple product 

    (3) Cross product 

    (4) Cross triple product 

    Correct option: 2

    Solution:

    For three vectors $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$ vector triple product is defined as $\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})$. $\vec{a} \times(\vec{b} \times \vec{c})=(\vec{a} \cdot \vec{c}) \cdot \vec{b}-(\vec{a} \cdot \vec{b}) \cdot \vec{c}$

    Hence, the answer is the option 2.

     

    Question 18: $\vec{a} \times(\vec{b}+\vec{c})=(\vec{a} \times \vec{b})+(\vec{a} \times \vec{c})$ Which property is it? 

    (1) Commutative 

    (2) Associative 

    (3) Distributive 

    (4) Equivalence 

    Correct option: 3

    Solution:

    $\vec{a} \times(\vec{b}+\vec{c})=(\vec{a} \times \vec{b})+(\vec{a} \times \vec{c})$

    Vector product is distributive

    Hence, the answer is the option 3.

     

    Question 19: $\vec{a} \times \vec{b}=\vec{c}$, then $\vec{a} \cdot \vec{c}=$ 

    (1) 0

    (2) 1

    (3) $|\vec{b}|$ 

    (4) $\vec{b}$ 

    Correct option: 1

    Solution

    $\vec{a} \times \vec{b}$ is perpendicular to $\vec{a}$ and $\vec{b}$
    wherein

    $
    \begin{aligned}
    & \text { If } \vec{a} \times \vec{b}=\vec{c} \\
    & \vec{c} \cdot \vec{a}=\vec{c} \cdot \vec{b}=0
    \end{aligned}
    $
    Hence, the answer is the option 1

    Question 20: If $\vec{a} \times \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$, then $\vec{b} \times \vec{a}=$ 

    (1) $\hat{i}-\hat{j}+2 \hat{k}$ 

    (2) $\frac{\hat{i}-\hat{j}+2 \hat{k}}{\sqrt{6}}$ 

    (3) $\hat{i}+\hat{j}+2 \hat{k}$ 

    (4) None of these 

    Correct option: 4

    Solution:

    The vector cross product satisfies the anti-commutative property:

    $
    \vec{a} \times \vec{b}=-(\vec{b} \times \vec{a})
    $
    Given:

    $
    \vec{a} \times \vec{b}=\hat{i}-\hat{j}+2 \hat{k},
    $

    we have:

    $
    \vec{b} \times \vec{a}=-(\hat{i}-\hat{j}+2 \hat{k})=-\hat{i}+\hat{j}-2 \hat{k}
    $

    Final Answer:

    $
    \vec{b} \times \vec{a}=-\hat{i}+\hat{j}-2 \hat{k}
    $

    Hence, the answer is the option 4

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    VITEEE Vector Algebra Important Topics 2027

    Vector Algebra carries 11% of the weightage of all maths chapters. While preparing for VITEEE, students must cover the following topics in Vector Algebra:

    Also Check: Most Scoring Topics in VITEEE| VITEEE Chapter-Wise Weightage 

    Important VITEEE Vector Algebra Formulas

    Before you solve VITEEE Vector Algebra Important Questions, it’s important to learn the basic vector formulas. These formulae are used quite often in numericals.

    1. For vector $\vec{A}=a \hat{i}+b \hat{j}+c \hat{k}$, the magnitude $|\vec{A}|=\sqrt{a^2+b^2+c^2}$

    2. Unit Vector: $\hat{A}=\frac{\vec{A}}{|\vec{A}|}$

    3. The position vector of $P(x, y, z)$, is $\overrightarrow{O P}=x \hat{i}+y \hat{j}+z \hat{k}$

    4. $\vec{A}+\vec{B}=\left(a_1+b_1\right) \hat{i}+\left(a_2+b_2\right) \hat{j}+\left(a_3+b_3\right) \hat{k}$

    5. $\vec{A}-\vec{B}=\left(a_1-b_1\right) \hat{i}+\left(a_2-b_2\right) \hat{j}+\left(a_3-b_3\right) \hat{k}$

    6. Distance between 2 vectors 

    $A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}$

    7. Dot products: $\vec{A} \cdot \vec{B}=|\vec{A}||\vec{B}| \cos \theta$

    8. Angle between 2 vectors: $\cos \theta=\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}$

    9. Cross product: $|\vec{A} \times \vec{B}|=|\vec{A}||\vec{B}| \sin \theta$

    10. Projection of One Vector on Another

    • Scaler: $\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}$

    • Vector: $\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B}$

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    11. Vector Triple Product:  $\vec{A} \times(\vec{B} \times \vec{C})=\vec{B}(\vec{A} \cdot \vec{C})-\vec{C}(\vec{A} \cdot \vec{B})$

    Also Check: VITEEE 2027 Important Formulas

    Preparation Tips for Vector Algebra in VITEEE

    Students need to be clear about the basics and formulae of Vector Algebra to prepare for VITEEE. Practice is the key to improving calculation ability and speed. Here are some easy tips that can help you prepare better:

    1. Learn basic concepts like vectors, magnitude, unit vectors, direction ratios and cosines.

    2. Go through the important formulas like dot product, cross product, angle between vectors and scalar triple product.

    3. Practice VITEEE Vector Algebra questions to get acquainted with various question formats.

    4. Practice calculations properly since calculation errors might give you the wrong answer.

    5. Do not forget to include Vector Algebra in your VITEEE mock test practice.

    Also Check: VITEEE 2027 Preparation Tips 

    VITEEE Syllabus: Subjects & Chapters
    Select your preferred subject to view the chapters

    Best Books for VITEEE Vector Questions

    While preparing vector questions for VITEEE, it is very important to follow the best books because they help properly cover all the concepts. 

    1. Class 11 Maths NCERT

    1. RD Sharma Objective Maths

    1. Cengage Maths 

    1. Arihant Skills in Maths

    1. Problems Plus in IIT Maths

    Why Practice VITEEE Vector Algebra MCQs

    There are various advantages of practising vector algebra problems:

    1. VITEEE Vector Algebra Questions will enhance your knowledge about various aspects of vectors.

    2. It will enable you to acquaint yourself with different types of questions.

    3. VITEEE Vector Algebra Practice Questions will increase your speed of calculations.

    4. It will assist in identifying areas that require further practice.

    Frequently Asked Questions (FAQs)

    Q: Is Vector Algebra helpful for VITEEE?
    A:

    Yes, it is one of those topics which must be covered while studying the mathematics subject in order to appear for the VITEEE.

    Q: What are the topics that can be covered in Vector Algebra for VITEEE?
    A:

    Topics like magnitude of vectors, unit vectors, dot product, cross product, angle between vectors, direction cosines, and scalar triple product can be studied.

    Q: How should I practise VITEEE Vector Algebra questions?
    A:

    Students can practise chapter-wise multiple-choice questions, previous year-like questions, test series, and quizzes online. This will not only make you better at solving questions but faster too.

    Q: Are Vector Algebra questions tough in VITEEE?
    A:

    This might depend on each individual's performance. Some questions are directly based on the formula whereas others involve calculation in several steps. Conceptual clarity of the topic can help solve them easily.

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    Questions related to VITEEE

    On Question asked by student community

    Have a question related to VITEEE ?

    Your age is not a problem . For example, the VITEEE 2026 age criterion required candidates to be born on or after 1 July 2004, so your DOB (6 February 2007) is well within the acceptable range.

    However, your Class 12 history may affect your eligibility .

    VIT's admission guidelines

    Hello Dear Student,

    The official VITEEE 2027 syllabus will be released along with the admission brochure, which is usually published a few months before the application process begins. The syllabus is generally based on the Class 11 and Class 12 curriculum.

    For preparation, NCERT textbooks should be your primary study

    Hello Dear Student,
    No, the VIT Engineering Entrance Examination (VITEEE) for the 2026 academic year is not available now

    You can check, find and access more information here: https://engineering.careers360.com/exams/viteee
    Hope it helps!

    Hello,

    With a VITEEE rank of around 69,000 , you have a good chance of getting CSE (AI & ML) at VIT-AP . Based on recent admission trends, CSE AI & ML at VIT-AP has been available up to around the 60,000–80,000 rank range depending on the fee category and

    Hello Dear Student,
    With a 69k rank in VITEEE, you are eligible for Category 4 or 5 to secure CSE with a specialization in AI/ML at the VIT AP campus. Category 1 and 2 seats typically close much earlier for Computer Science branches.

    You can check, find and access more