# 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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