Find, correct to two decimal places, the acute angle between (p = begin{pmatrix} 13 \ 14 end{pmatrix}) and (q = begin{pmatrix} 12 \ 5 end{pmatrix}).
-
A.
23.52° -
B.
24.50° -
C.
29.52° -
D.
29.82°
Correct Answer: Option B
Explanation
(p . q = |p||q|cos theta)
(156 + 70 = (sqrt{13^{2} + 14^{2}})(sqrt{12^{2} + 5^{2}}) cos theta)
(226 = (sqrt{365})(13) cos theta)
(frac{226}{13sqrt{365}} = cos theta)
(cos theta = 0.9099)
(theta = 24.50°)