Find the Component Form of Vector V Given Its Magnitude $\| \mathbf { v } \| = 7 \text { and the angle it }$

Multiple Choice

Find the component form of vector v given its magnitude is $\| \mathbf { v } \| = 7 \text { and the angle it }$ makes with the positive $x$ -axis is $\theta = 120 ^ { \circ }$ .

A) $\left( \frac { 7 \sqrt { 3 } } { 2 } , \frac { 7 \sqrt { 3 } } { 4 } \right)$
B) $\left( - \frac { \sqrt { 5 } } { 3 } , 7 \frac { \sqrt { 3 } } { 3 } \right)$
C) $\left( \frac { 7 \sqrt { 3 } } { 4 } , \frac { 7 \sqrt { 3 } } { 4 } \right)$
D) $\left( - \frac { 7 } { 2 } , 7 \frac { \sqrt { 3 } } { 2 } \right)$
E) $\left( \frac { 7 } { 2 } , \frac { 7 \sqrt { 5 } } { 2 } \right)$