Page 3 - Lesson Notes (Motion in a Plane)

Vertical component A y = A sin θ

2
2
Magnitude of vector A = √A x + A y
tan θ = A y / A x

Subtraction of Vectors

Subtraction of a vector B from a vector A is defined as the addition of vector -B (negative of
vector B) to vector AThus, A – B = A + (-B)

Multiplication of a Vector
1. By a Real Number
When a vector A is multiplied by a real number n, then its magnitude becomes n times but
direction and unit remains unchanged.

Scalar or Dot Product of Two Vectors
The scalar product of two vectors is equal to the product of their magnitudes and the
cosine of the smaller angle between them. It is denoted by . (dot).

A * B = AB cos θ

The scalar or dot product of two vectors is a scalar.

Properties of Scalar Product
(i) Scalar product is commutative, i.e., A * B= B * A
(ii) Scalar product is distributive, i.e., A * (B + C) = A * B + A * C
(iii) Scalar product of two perpendicular vectors is zero.

A * B = AB cos 90° = O
(iv) Scalar product of two parallel vectors is equal to the product of their magnitudes, i.e., A * B = AB cos
0° = AB
(v) Scalar product of a vector with itself is equal to the square of its magnitude, i.e.,

A * A = AA cos 0° = A 2
(vi) Scalar product of orthogonal unit vectors

and