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Calculate, correct to the nearest degree, the angle between ...

Calculate, correct to the nearest degree, the angle between the vectors (131) and (14)

A.

58°

B.

72°

C.

74°

D.

87°

Correct answer is B

a.b=|a||b|cosθ

(131).(14)=13×1+1×4=13+4=17

17=(132+12)(12+42)cosθ

17=(170)(17)cosθ

cosθ=171710=1010=0.3162

\theta = \cos^{-1} 0.3162 = 72°