Find the angle between the vectors $\mathbf { u }$ and $\mathbf { v }$. Express your answer in degrees and round to the nearest tenth of a degree.
$$\mathbf { u } = \langle - 3,6,3 \rangle , \mathbf { v } = \langle 9,9,9 \rangle$$
A) $25.2 ^ { \circ }$
B) $28.1 ^ { \circ }$
C) $64.8 ^ { \circ }$
D) $90 ^ { \circ }$
E) $61.9 ^ { \circ }$

Question

Quizplus · Accepted Answer

We use the formula $\cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\| \|\mathbf{v}\|}$ to find the angle between the vectors. We get $\cos \theta = \frac{-27+54+27}{\sqrt{54}\sqrt{243}}$, so $\cos \theta = \frac{\sqrt{6}}{3}$. Taking the inverse cosine, we get $\theta \approx 61.9 ^{\circ}$. Therefore, the answer is $\boxed{\text{(E)}}$.

Find the Angle Between the Vectors u\mathbf { u }u And v\mathbf { v }v

Find the Angle Between the Vectors $\mathbf { u }$ And $\mathbf { v }$