Find the angle between \((5i + 3j)\) and \((3i – 5j)\).

Explanation

\(a . b = |a||b|\cos \theta\)

\(\cos \theta = \frac{a . b}{|a||b|}\)

= \( \frac{(5i + 3j).(3i - 5j)}{(\sqrt{5^2 + 3^2})(\sqrt{3^{2} + (-5)^{2}})}\)

= \(\frac{0}{34} = 0\)

\(\theta = \cos^{-1} 0 = 90°\)