If (x = i – 3j) and (y = 6i + j), calculate the angle between x and y.
-
A.
60° -
B.
75° -
C.
81° -
D.
85°
Correct Answer: Option C
Explanation
(overrightarrow{x} . overrightarrow{y} = |overrightarrow{x}||overrightarrow{y}|costheta)
(overrightarrow{x} . overrightarrow{y} = (i – 3j) . (6i + j) = 6 – 3 = 3)
(|overrightarrow{x}| = sqrt{1^{2} + (-3)^{2}} = sqrt{10})
(|overrightarrow{y}| = sqrt{6^{2} + 1^{2}} = sqrt{37})
(therefore 3 = (sqrt{10})(sqrt{37})cos theta)
(costheta = frac{3}{sqrt{370}} = 0.1559)
(theta = cos^{-1} 0.1559 approxeq 81°)