Write a Vector in Terms of Its Magnitude and Direction
-$$\| \mathbf { v } \| = 7 , \quad \theta = 225 ^ { \circ }$$
A) $\mathbf { v } = - \frac { 7 \sqrt { 2 } } { 2 } \mathrm { i } - \frac { 7 \sqrt { 2 } } { 2 } \mathrm { j }$
B) $v = - \frac { 7 \sqrt { 3 } } { 2 } i - \frac { 7 } { 2 } j$
C) $v = - \frac { 7 } { 2 } \mathbf { i } - \frac { 7 \sqrt { 3 } } { 2 } \mathrm { j }$
D) $v = \frac { 7 \sqrt { 2 } } { 2 } i + \frac { 7 \sqrt { 2 } } { 2 } j$

Question

Quizplus · Accepted Answer

The vector's magnitude is 7 and its direction is 225°, which is in the third quadrant where both x and y components are negative. Using trigonometry, the components can be found as $7\cos(225^\circ)$ and $7\sin(225^\circ)$, both of which equal $-\frac{7\sqrt{2}}{2}$, matching option A.

Write a Vector in Terms of Its Magnitude and Direction ∥v∥=7,θ=225∘\| \mathbf { v } \| = 7 , \quad \theta = 225 ^ { \circ }∥v∥=7,θ=225∘

Write a Vector in Terms of Its Magnitude and Direction $\| \mathbf { v } \| = 7 , \quad \theta = 225 ^ { \circ }$