Calculate, correct to the nearest degree, the angle between the vectors (begin{pmatrix} 13 \ 1 end{pmatrix}) and (begin{pmatrix} 1 \ 4 end{pmatrix}).
-
A.
58° -
B.
72° -
C.
74° -
D.
87°
Correct Answer: Option B
Explanation
(a . b = |a||b| cos theta)
(begin{pmatrix} 13 \ 1 end{pmatrix}. begin{pmatrix} 1 \ 4 end{pmatrix} = 13 times 1 + 1 times 4 = 13 + 4 = 17)
(17 = (sqrt{13^{2} + 1^{2}})(sqrt{1^{2} + 4^{2}}) cos theta)
(17 = (sqrt{170})(sqrt{17}) cos theta)
(cos theta = frac{17}{17sqrt{10}} = frac{sqrt{10}}{10} = 0.3162)
(theta = cos^{-1} 0.3162 = 72°)