Two vectors m and n are defined by \(m = 3i + 4j\) and \(n = 2i - j\). Find the angle between m and n.
A. 97.9°
B. 79.7°
C. 63.4°
D. 36.4°
Correct Answer: B
Explanation
\(m . n = |m||n|\cos \theta\)
\((3i + 4j) . (2i - j) = 6 - 4 = 2\)
\(2 = |(3i + 4j)||(2i - j)| \cos \theta\)
\(|3i + 4j| = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\)
\(|2i - j| = \sqrt{2^{2} + (-1)^{2}} = \sqrt{5}\)
\(2 = 5(\sqrt{5})(\cos \theta)\)
\(\cos \theta = \frac{2}{5\sqrt{5}} = 0.08\sqrt{5}\)
\(\theta = \cos^{-1} 0.1788 = 79.7°\)
