Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .
A)? $\| \mathbf { v } \| = \sqrt { 6 } ; \theta = 80 ^ { \circ }$
B)? $\| \mathbf { v } \| = 6 ; \theta = 100 ^ { \circ }$
C)? $\| \mathbf { v } \| = 6 ; \theta = 80 ^ { \circ }$
D)? $\| \mathbf { v } \| = 6 ; \theta = 10 ^ { \circ }$
E)? $\| \mathbf { v } \| = \sqrt { 6 } ; \theta = 100 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of $\mathbf{v}$ is given by the coefficient $6$, as the vector components are already unit vectors in their respective directions. The direction angle $\theta$ is directly given as $80^\circ$, matching the angles used in the cosine and sine functions.

Find the Magnitude and Direction Angle Of v=6(cos⁡80∘i+sin⁡80∘j)\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)v=6(cos80∘i+sin80∘j)

Find the Magnitude and Direction Angle Of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$