Find the angle between the pair of vectors to the nearest tenth of a degree.
-$$7 \mathbf { i } - 5 \mathbf { j } , 2 \mathbf { i } - 6 \mathbf { j }$$
A) $36.0 ^ { \circ }$
B) $44.4 ^ { \circ }$
C) $117.2 ^ { \circ }$
D) $104.7 ^ { \circ }$

Question

Quizplus · Accepted Answer

The dot product of the two vectors is $$(7)(2)+(-5)(-6)=14+30=44$$The magnitude of the first vector is $$\sqrt{7^2+(-5)^2}=\sqrt{49+25}=\sqrt{74}$$The magnitude of the second vector is $$\sqrt{2^2+(-6)^2}=\sqrt{4+36}=\sqrt{40}$$The angle between the two vectors is $$	heta=\cos^{-1}\left(\frac{44}{\sqrt{74}\sqrt{40}}ight)\approx36.0^\circ$$

Find the Angle Between the Pair of Vectors to the Nearest