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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