if the volume of a parallelpiped whose adjacent egges are `veca=2hati+3hatj+4hatk,vecb=hati+alphahatj+2hatk, vecc=veci+2hatj + alphahatk is 15` then find of `alpha if (alpha gt 0) `

Explanation

To solve the problem, we need to find the value of α given that the volume of the parallelepiped formed by the vectors **a**, **b**, and **c** is 15. The vectors are defined as follows:

- **a** = 2i + 3j + 4k
- **b** = i + αj + 2k
- **c** = i + 2j + αk

The volume of the parallelepiped can be calculated using the scalar triple product, which can be represented as the determinant of a 3x3 matrix formed by the components of the vectors.

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