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

`|{:(2,3,4),(1 , alpha,2),(1,2,alpha):}|=15`
`or 2(alpha^(2)-4)+3(2-alpha)+ 4(2-alpha) =15`
`or 2 alpha^(2)-8 + 6 -3alpha=8 - 4alpha = 15`
`or 2alpha^(2) - 9alpha=2alpha-9=0`
` or ( alpha+1) (2 alpha-9) =0`
`or alpha = -1 , 9//2`