Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$\{ - 10,4 \}$$ and $$( 8,4 )$$
A) $72 , - 41 ^ { \circ } 38 ^ { \prime }$
B) $- 96,131 ^ { \circ } 33 ^ { \prime }$
C) $4,096,131 ^ { \circ } 40 ^ { \prime }$
D) $- 64,131 ^ { \circ } 38 ^ { \prime }$
E) $- 64 , - 41 ^ { \circ } 33 ^ { \prime }$

Question

Quizplus · Accepted Answer

The dot product is $(-10)(8) + (4)(4) = -80 + 16 = -64$. The magnitudes are $\sqrt{(-10)^2 + 4^2} = \sqrt{116}$ and $\sqrt{8^2 + 4^2} = \sqrt{80}$. The cosine of the angle is $\frac{-64}{\sqrt{116} \times \sqrt{80}}$, which gives an angle of approximately $131^\circ 38'$.

Find (A) the Dot Product of the Two Vectors and (B)