Find the vector $\mathbf { Y }$ having length $| \mathrm { v } | = 4$
, and direction $\theta = 225 ^ { \circ }$
A) $\mathrm { v } = \langle - 1,1 \rangle$
B) $\mathrm { v } = \langle - 2 \sqrt { 2 } , - 2 \sqrt { 2 } \rangle$
C) $\mathrm { v } = \langle - \sqrt { 2 } , \sqrt { 2 } \rangle$
D) $\mathbf {v } = \langle 1,1 \rangle$
E) $\mathrm { v } = \langle - 2,2 \rangle$

Question

Quizplus · Accepted Answer

The vector with a length of 4 and a direction of 225 degrees from the positive x-axis in standard position would have components equal in magnitude but opposite in sign, pointing in the southwest direction. The correct components can be found using trigonometry: $4\cos(225^\circ) = -2\sqrt{2}$ and $4\sin(225^\circ) = -2\sqrt{2}$, making option B the correct choice.

Find the Vector Y\mathbf { Y }Y Having Length ∣v∣=4| \mathrm { v } | = 4∣v∣=4

Find the Vector $\mathbf { Y }$ Having Length $| \mathrm { v } | = 4$