Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis.
-$$\| v \| = 7 , \alpha = 60 ^ { \circ }$$
A) $\mathbf { v } = 7 \left( - \frac { 7 } { 2 } \mathbf { i } - \frac { 7 \sqrt { 3 } } { 2 } \mathrm { j } \right)$
B) $v = 7 \left( \frac { 7 \sqrt { 3 } } { 2 } \mathbf { i } + \frac { 7 } { 2 } \mathrm { j } \right)$
C) $v = 7 \left( \frac { \sqrt { 2 } } { 2 } i + \frac { \sqrt { 2 } } { 2 } j \right)$
D) $v = 7 \left( \frac { 7 } { 2 } i + \frac { 7 \sqrt { 3 } } { 2 } j \right)$

Question

Quizplus · Accepted Answer

The vector $v$ in the form $ai + bj$ can be found using the magnitude of $v$ and the angle $\alpha$ it makes with the positive x-axis. The components of $v$ are given by $v_x = \|v\| \cos(\alpha)$ and $v_y = \|v\| \sin(\alpha)$. For $\|v\| = 7$ and $\alpha = 60^\circ$, we have $v_x = 7 \cos(60^\circ) = 7 \times \frac{1}{2} = \frac{7}{2}$ and $v_y = 7 \sin(60^\circ) = 7 \times \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}$. Therefore, $v = \frac{7}{2}i + \frac{7\sqrt{3}}{2}j$.

Write the Vector V in the Form Ai + Bj ∥v∥=7,α=60∘\| v \| = 7 , \alpha = 60 ^ { \circ }∥v∥=7,α=60∘

Write the Vector V in the Form Ai + Bj $\| v \| = 7 , \alpha = 60 ^ { \circ }$