Given unit vectors `hatm hatn and hatp` such that angle between `hatm and hat n is alpha` and angle between `hatp and hatm X hatn is alpha `if [n p m] = 1/4 find alpha

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
We have three unit vectors: \(\hat{m}, \hat{n}, \hat{p}\). The angle between \(\hat{m}\) and \(\hat{n}\) is \(\alpha\). The angle between \(\hat{p}\) and \(\hat{m} \times \hat{n}\) is also \(\alpha\). We are given that the scalar triple product \([\hat{n}, \hat{p}, \hat{m}] = \frac{1}{4}\).

2. **Using the Scalar Triple Product:**
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