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If vector (hata+ 2hatb) is perpendicular...

If vector `(hata+ 2hatb)` is perpendicular to vector `(5hata-4hatb)`, then find the angle between `hata and hatb`.

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To solve the problem, we need to find the angle between the unit vectors \( \hat{a} \) and \( \hat{b} \) given that the vector \( \hat{a} + 2\hat{b} \) is perpendicular to the vector \( 5\hat{a} - 4\hat{b} \). ### Step-by-step Solution: 1. **Understanding Perpendicular Vectors**: Since the vectors \( \hat{a} + 2\hat{b} \) and \( 5\hat{a} - 4\hat{b} \) are perpendicular, their dot product must equal zero: \[ (\hat{a} + 2\hat{b}) \cdot (5\hat{a} - 4\hat{b}) = 0 ...
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