Find the angle between \((5i + 3j)\) and \((3i - 5j)\).
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Correct Answer: Option B
Explanation:
\(a . b = |a||b|\cos \theta\)
\(\cos \theta = \frac{a . b}{|a||b|}\)
= \( \frac{(5i + 3j).(3i - 5j)}{(\sqrt{5^2 + 3^2})(\sqrt{3^{2} + (-5)^{2}})}\)
= \(\frac{0}{34} = 0\)
\(\theta = \cos^{-1} 0 = 90°\)
\(a . b = |a||b|\cos \theta\)
\(\cos \theta = \frac{a . b}{|a||b|}\)
= \( \frac{(5i + 3j).(3i - 5j)}{(\sqrt{5^2 + 3^2})(\sqrt{3^{2} + (-5)^{2}})}\)
= \(\frac{0}{34} = 0\)
\(\theta = \cos^{-1} 0 = 90°\)