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Scalars And Vectors - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • 47 Questions around this concept.

Solve by difficulty

For a physical quantity which of following is true for numerical value for two system C.G.S and MKS -

If we multiply any vector by -3 then?

The quantities that only have magnitude and do not have direction are called -

Which of the following is a scalar quantity ?

If two vectors are collinear then

If two vectors have the same starting point then vectors called as 

If two vectors have equal magnitude and the same direction then vectors are called. 

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If two vectors have the following properties then the vectors are called

$
|\vec{A}|=|\vec{B}| \quad \vec{A}=-\vec{B}
$

If $\vec{P}=x \hat{i}+y \hat{j}+3 \hat{k}$ and $\vec{Q}=4 \hat{i}+2 \hat{j}+\alpha \hat{k}$ are equal vectors then values of $\mathrm{x}, \mathrm{y}, \mathrm{z}$ and $\alpha$ are

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Which of the following is a scalar quantity ? 

Concepts Covered - 1

Scalars and vectors
  1. Scalars

Physical quantities can be described completely by their magnitude only but no particular direction.

Examples- Distance, speed, work, charges, temperatureetc.

Tips for scalars-

  • Scalar quantities can be positive, negative or zero.

  • Represented by alphabet only A, B, C.

  • These physical quantities follow normal algebraic rules of addition.

  1.  Vectors

Physical quantities can be described by their magnitude and direction.

Physical quantities like Displacement, force, velocity etc. are vectors.

Tips of vectors-

  • Vectors can be positive, negative or zero.

  • Represented by alphabet having an arrow on their head.

         $\vec{A}, \vec{B}, \vec{C}$

  •   These physical quantities follow the laws of vector addition.

  •  Types of vectors

  1.  Equal vectors-

            Two vectors are said to be equal if they have equal magnitude and the same directions.

       

$
\begin{aligned}
& \longrightarrow \vec{A} \\
& \longrightarrow \vec{B} \\
& \vec{A}=\vec{B}
\end{aligned}
$

The angle between these two vectors $\Theta$ is equal to zero.

  1. Negative vectors-

              Two vectors are said to be negative with respect to each other if they have equal magnitude but opposite directions.

      

$
\begin{aligned}
& \rightarrow \vec{A} \\
& \leftarrow \vec{B} \\
& \vec{A}=-\vec{B}
\end{aligned}
$


The angle between negative vectors is equal to 180 . i.e $\Theta=180^{\circ}$
3. Collinear vectors-

Two vectors are said to be collinear if they have a common line of action.
a. If two vectors are collinear and parallel then the angle between them is zero.
b. If two vectors are collinear and anti-parallel then the angle between them is $180^{\circ}$.

So, Angle between collinear vectors A \& B is either zero or $180^{\circ}$.

$
\text { i.e; } \Theta=0^{\circ} \text { or } 180^{\circ}
$
 

  1. Co-initial vectors-

                Two vectors are said to be Co-initial vectors if they have the same initial point.

 

 

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Scalars and vectors

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