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If vec(a)andvec(b) are two unit vectors ...

If `vec(a)andvec(b)` are two unit vectors such that `vec(a) + 2vec(b) and 5vec(a) - 4vec(b)` are perpendicupar to each other, then the angle between `vec(a) and vec(b)` is

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To find the angle between the two unit vectors \( \vec{a} \) and \( \vec{b} \), we start by using the information given in the problem. We know that the vectors \( \vec{a} + 2\vec{b} \) and \( 5\vec{a} - 4\vec{b} \) are perpendicular to each other. This means that their dot product is equal to zero. ### Step-by-Step Solution: 1. **Write the condition for perpendicular vectors**: \[ (\vec{a} + 2\vec{b}) \cdot (5\vec{a} - 4\vec{b}) = 0 \] ...
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