Vector Addition And Vector Subtraction - Practice Questions & MCQ

• 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.

2.  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.