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Vector Addition And Vector Subtraction - Practice Questions & MCQ

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

Quick Facts

  • Vector addition and Vector Subtraction is considered one of the most asked concept.

  • 64 Questions around this concept.

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Two forces are such that the sum of their magnitude is 18N, and their resultant is 12N which is perpendicular to the smaller force. Then the magnitude of the forces are

A particle is moving along north after moving for 2 sec with a speed of 4 m/s, its speed becomes 5m/s.What is its displacement (in meters) at end of 7 sec

Which of the following relations is true for two unit vector $\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}$ making an angle $\theta$ to each other ?

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A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $\theta$ is :

Two vectors \vec{A}  and \vec{B} inclined at an angle \theta have a resultant \vec{R}\ which makes an angle \alpha with \vec{A}. If the direction of \vec{A}and \vec{B} are interchanged, the resultant will have the same:

 Which of the following is not a property of the null vector

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\left| \vec{A}+\vec{B} \right|=\left| \vec{A}-\vec{B} \right| then the angle between \vec{A}\And \vec{B} will be :

If $\vec{P}=3 \hat{i}+4 \hat{j}+7 \hat{k}$ and $\vec{Q}=\hat{i}+2 \hat{j}+\hat{k}$ the value of magnitude of resolution of $\vec{P}-\vec{Q}$ is.

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If $\vec{A}$ and $\vec{B}$ are non zero vectors. Which obey the relation $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$ then the angle between them is -

 

Concepts Covered - 1

Vector addition and Vector Subtraction
  • For the simple case in which both vectors have the same direction
  1. Vector addition-

  •  Vectors quantities are not added according to simple algebraic rules, because their direction that matters.

  • The addition of vectors means determining their resultant.

  • When two vectors are in the same direction then upon addition the direction of the resultant vector is the same as any of the two vectors, while the magnitude of the resultant vector is simply the algebraic sum of two vectors.

  • -eg, Vector $\vec{A}$ has magnitude $4 \&$ vector $\vec{B}$ has magnitude 2 in the same direction.
    $\vec{A}+\vec{B}=4+2=6$ So resultant has a magnitude equal to 6 while its direction is either along $\vec{A}$ or $\vec{B}$
    2) Vector Subtraction-
    - Vector subtraction of $\vec{B}$ from $\vec{A}$ is equal to Vector addition of $\vec{A}$ and negative vector of $\vec{B}$.

    $
    \vec{A}-\vec{B}=\vec{A}+(-\vec{B})
    $

    - E.g., Vector $\vec{A}$ and $\vec{B}$ are in east direction with magnitudes 4 and 2 respectively.

    Vector subtraction of $\vec{B}$ from $\vec{A}$ is equal

    $
    =\vec{A}-\vec{B}=4-2=2
    $


    The resultant vector has a magnitude of 2 in the east direction.
    - For the case when both vectors do not have the same direction

 

  1. Triangle law of vector addition

  If two vectors are represented by both magnitude and direction by two sides of a triangle taken in the same order then their resultant is represented by side of the triangle. 

The figure represents the triangle law of vector addition

So resultant  side C is given by 

$
c=\sqrt{a^2+b^2+2 a b \cos \theta}
$


Where $\theta=$ angle between two vectors.

  1.  Parallelogram law of vector addition 

  • If two vectors are represented by both magnitude and direction by two adjacent sides of a parallelogram taken from the same point then their resultant is also represented by both magnitude and direction taken from the same point but by diagonal of the parallelogram.

 The figure represents law of parallelogram vector Addition

  • Commutative law-

The Sum of vectors remains the same in whatever order they may be added.

$\vec{P}+\vec{Q}=\vec{Q}+\vec{P}$

Fig. Shows Commutative law of vector addition.

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Vector addition and Vector Subtraction

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