Vector A with rightwards arrow on top has a magnitude of 12m and its direction is 120o counterclockwise from the x axis. What are the magnitude and direction of the vector minus 2 A with rightwards arrow on top? The direction is represented by a counterclockwise angle from the + x axis

(A) 24m, - 120o

(B) 24m, - 300o

(C) - 24m, - 120o

(D) 24m, 300o

(E) - 24m, 300o

D) 24m, 300o

Explanation:

The vector A has magnitude of 12 m and it makes 120 degree with + ve x axis

So it can be represented by the vector as follows

A = 12 Cos 120 i + 12 sin 120 j

vector 2A = 24 Cos 120 i + 24 sin 120 j

- 2A = - 24 Cos 120 i - 24 sin 120 j

= 24 Cos (180 - 120) - 24 sin (180 - 120)

= 24 Cos 60 - 24 sin 60

= 24 Cos (360 - 60) + 24 sin (360 - 60)

= 24 Cos 300 + 24 sin 300

It represents a vector having magnitude of 24 and making 300 degree with + ve x - axes in anticlockwise direction.