Write the vector v in the form ai + bj, given its magnitude v and the angle  it makes with the positive x-axis.
-$$\| \mathbf { v } \| = 15 , \alpha = 45 ^ { \circ }$$
A) $\mathbf { v } = 15 \left( \frac { 15 \sqrt { 3 } } { 2 } \mathbf { i } + \frac { 15 } { 2 } \mathbf { j } \right)$
B) $\mathbf { v } = 15 \left( \frac { 15 } { 2 } \mathrm { i } + \frac { 15 \sqrt { 3 } } { 2 } \mathrm { j } \right)$
C) $v = 15 \left( - \frac { \sqrt { 2 } } { 2 } i - \frac { \sqrt { 2 } } { 2 } j \right)$
D) $\mathbf { v } = 15 \left( \frac { \sqrt { 2 } } { 2 } \mathrm { i } + \frac { \sqrt { 2 } } { 2 } \mathrm { j } \right)$

Question

Quizplus · Accepted Answer

The vector $\mathbf{v}$ can be expressed in terms of its magnitude and direction using the cosine and sine of the angle it makes with the positive x-axis. For an angle of $45^\circ$, both $\cos(45^\circ)$ and $\sin(45^\circ)$ equal $\frac{\sqrt{2}}{2}$. Therefore, the vector $\mathbf{v}$ in the form $ai + bj$ is $15\left(\frac{\sqrt{2}}{2}i + \frac{\sqrt{2}}{2}j\right)$, matching option D.

Write the Vector V in the Form Ai + Bj ∥v∥=15,α=45∘\| \mathbf { v } \| = 15 , \alpha = 45 ^ { \circ }∥v∥=15,α=45∘

Write the Vector V in the Form Ai + Bj $\| \mathbf { v } \| = 15 , \alpha = 45 ^ { \circ }$