Given unit vectors ` hat m , hat n and hat p` such that angel between ` hat m and hat n` is `alpha` and angle between ` hat p and( hat mxx hat n)` is also `alpha,then[ hat n hat p hat m]=`

Explanation

`[hatn hatp hatm] = [hatp hatm hatn] `
` = hatp . (hatm xxhatn)`
`= |hatp|.|hatm xx hatn|cos alpha`
`= |hatm xx hatn| cos alpha`
`= sin alpha cos alpha = 1//4`
`Rightarrow sin 2 alpha = 1//2`
` or 2 alpha = 30^(@)`
`or alpha = 15 ^(@)`