Find the angle between v and w. Round to one decimal place, if necessary.
-$\mathbf { v } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ and $\mathbf { w } = \mathbf { i } + 3 \mathbf { j } - 3 \mathbf { k }$
A) $32.7 ^ { \circ }$
B) $55.6 ^ { \circ }$
C) $57.3 ^ { \circ }$
D) $67.3 ^ { \circ }$

Question

Quizplus · Accepted Answer

The dot product of v and w is $$(2)(1) + (1)(3) + (-2)(-3) = 2 + 3 + 6 = 11$$The magnitudes of v and w are $$\Vert \mathbf { v } \Vert = \sqrt { 2 ^ { 2 } + 1 ^ { 2 } + ( - 2 ) ^ { 2 } } = \sqrt { 9 } = 3$$$$\Vert \mathbf { w } \Vert = \sqrt { 1 ^ { 2 } + 3 ^ { 2 } + ( - 3 ) ^ { 2 } } = \sqrt { 19 }$$So the angle between v and w is $$\cos 	heta = \frac { \mathbf { v } \cdot \mathbf { w } } { \Vert \mathbf { v } \Vert \Vert \mathbf { w } \Vert } = \frac { 11 } { 3 \sqrt { 19 } } \approx 0.845$$$$	heta \approx \cos ^ { - 1 } ( 0.845 ) \approx 32.7 ^ { \circ }$$

Find the Angle Between V and W v=2i+j−2k\mathbf { v } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }v=2i+j−2k

Find the Angle Between V and W $\mathbf { v } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$