Find the angle between the vectors with the direction ratios proportional to 4, -3, 5 and 3, 4, 5.

Solution :

We have,

\(\vec{a}\) = \(4\hat{i} – 3\hat{j} + 5\hat{k}\) and \(\vec{b}\) = \(3\hat{i} + 4\hat{j} + 5\hat{k}\)

Let \(\theta\) is the angle between the given vectors. Then,

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

\(\implies\) cos\(\theta\) = \(12 – 12 + 25\over \sqrt{16 + 9 + 25} \sqrt{16 + 9 + 25}\) = \(1\over 2\)

\(\implies\) \(\theta\) = \(\pi\over 3\)


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