Question

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

Answer 1

D) 24m, 300o

Step-by-step 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.