Find the direction of the vector $v = 6 i + 6 \sqrt { 3 } \mathbf { j }$
A) $\theta = 30 ^ { \circ }$
B) $\theta = 150 ^ { \circ }$
C) $\theta = 120 ^ { \circ }$
D) $\theta = 210 ^ { \circ }$
E) $\theta = 60 ^ { \circ }$

Question

Quizplus · Accepted Answer

To find the direction of a vector, we need to find the angle it makes with the positive x-axis. We can use trigonometry to do this. Let $	heta$ be the angle between the vector and the positive x-axis. Then we have:

$$	an	heta = \frac{6\sqrt{3}}{6} = \sqrt{3}$$

Taking the inverse tangent of both sides, we get:

$$	heta = 	an^{-1}\sqrt{3} = 60^\circ$$

Therefore, the direction of the vector is $\boxed{	extbf{(E)}}$.

Find the Direction of the Vector v=6i+63jv = 6 i + 6 \sqrt { 3 } \mathbf { j }v=6i+63​j

Find the Direction of the Vector $v = 6 i + 6 \sqrt { 3 } \mathbf { j }$