Find the component form of $\mathbf { v }$ if $\| \mathbf { v } \| = 8$ and the angle it makes with the $x$-axis is $120 ^ { \circ }$.
A) $\langle - 4 \sqrt { 3 } , 4 \rangle$
B) $\langle - 8,8 \sqrt { 3 } \rangle$
C) $\langle - 8 \sqrt { 3 } , - 8 \rangle$
D) $\langle - 4,4 \sqrt { 3 } \rangle$
E) $\langle - 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question

Quizplus · Accepted Answer

We can use the fact that $\cos 120^\circ = -\frac{1}{2}$ and $\sin 120^\circ = \frac{\sqrt{3}}{2}$ to get $v_x = 8\cos 120^\circ = -4$, $v_y = 8\sin 120^\circ = 4\sqrt{3}$. Thus, the component form of $\mathbf{v}$ is $\boxed{\langle -4,4\sqrt{3}\rangle}$.

Find the Component Form Of v\mathbf { v }v If ∥v∥=8\| \mathbf { v } \| = 8∥v∥=8

Find the Component Form Of $\mathbf { v }$ If $\| \mathbf { v } \| = 8$