Find the angle between $\mathbf { u } $ and $\mathbf { Y }$
) $\mathbf { u } = \langle - 5,3 ) , \mathbf { v } = ( \sqrt { 2 } , 7 )$
A) $46.3 ^ { \circ }$
B) $80.6 ^ { \circ }$
C) $70.46 ^ { \circ }$
D) $19.5 ^ { \circ }$
E) $33.46 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angle between two vectors is given by the formula $\theta = \cos^{-1} \left(\frac{\mathbf{u} \cdot \mathbf{v}}{\Vert \mathbf{u} \Vert \Vert \mathbf{v} \Vert}\right)$. Plugging in the given values, we get:$\theta = \cos^{-1} \left(\frac{(-5)(\sqrt{2}) + (3)(7)}{\sqrt{(-5)^2 + 3^2} \sqrt{(\sqrt{2})^2 + 7^2}}\right)$$\theta = \cos^{-1} \left(\frac{-5\sqrt{2} + 21}{\sqrt{34} \sqrt{50}}\right)$$\theta = \cos^{-1} \left(\frac{21 - 5\sqrt{2}}{\sqrt{1700}}\right)$$\theta = \cos^{-1} \left(\frac{21 - 5\sqrt{2}}{41.23}\right)$$\theta = \cos^{-1} (0.3346)$$\theta = 70.46^\circ$

Find the Angle Between u\mathbf { u } u And Y\mathbf { Y }Y

Find the Angle Between $\mathbf { u }$ And $\mathbf { Y }$