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

Question

Quizplus · Accepted Answer

The vector $v$ in the form $ai + bj$ can be found using the magnitude $v = 7$ and the angle $\alpha = 60^\circ$ with the positive x-axis. The components are $a = v\cos(\alpha)$ and $b = v\sin(\alpha)$. For $\alpha = 60^\circ$, $\cos(60^\circ) = \frac{1}{2}$ and $\sin(60^\circ) = \frac{\sqrt{3}}{2}$. Thus, $a = 7 \cdot \frac{1}{2} = \frac{7}{2}$ and $b = 7 \cdot \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}$, making the vector $v = \frac{7}{2}i + \frac{7\sqrt{3}}{2}j$.

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

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