Two vectors m and n are defined by (m = 3i + 4j) and (n…

Two vectors m and n are defined by (m = 3i + 4j) and (n = 2i – j). Find the angle between m and n.

Correct Answer: Option B

Explanation

(m . n = |m||n|cos theta)

((3i + 4j) . (2i – j) = 6 – 4 = 2)

(2 = |(3i + 4j)||(2i – j)| cos theta)

(|3i + 4j| = sqrt{3^{2} + 4^{2}} = sqrt{25} = 5)

(|2i – j| = sqrt{2^{2} + (-1)^{2}} = sqrt{5})

(2 = 5(sqrt{5})(cos theta))

(cos theta = frac{2}{5sqrt{5}} = 0.08sqrt{5}) 

(theta = cos^{-1} 0.1788 = 79.7°)