Page 2 - Lesson Notes (Motion in a Plane)

(xi) Position Vector A vector representing the straight line distance and the direction of any point or
object with respect to the origin, is called position vector.

Addition of Vectors

1. Triangle Law of Vectors
If two vectors acting at a point are represented in magnitude
and direction by the two sides of a triangle taken in one order,
then their resultant is represented by the third side of the
triangle taken in the opposite order. If two vectors A and B
acting at a point are inclined at an angle θ, then their resultant
R = √A2 + B2 + 2AB cos θ
If the resultant vector R subtends an angle β with vector A, then
tan β = B sin θ / A + B cos θ

2. Parallelogram Law of Vectors
If two vectors acting at a point are represented in magnitude and direction by the two adjacent
sides of a parallelogram draw from a point, then their resultant is represented in magnitude and
direction by the diagonal of the parallelogram draw from the same point.

Resultant of vectors A and B is given by R = √A + B + 2AB cos θ
If the resultant vector R subtends an angle β with vector A, then
tan β = B sin θ / A + B cos θ
3. Polygon Law of Vectors
It states that if number of vectors acting on a particle at a time
is represented in magnitude and direction by the various sides
of an open polygon taken in same order, their resultant vector R
is represented in magnitude and direction by the closing side of
polygon taken in opposite order.
R = A + B + C + D + E
Properties of Vector Addition
(i) Vector addition is commutative, i.e., A + B = B + A
(ii) Vector addition is associative, i.e.,A +(B + C)= B + (C + A)= C + (A + B)
(iii) Vector addition is distributive, i.e., m (A + B) = m A + m B

Resolution of a Vector into Rectangular Components

If any vector A subtends an angle θ with x-axis, then its

Horizontal component A x = A cos θ