If the volume of a parallelepiped whose adjacent edges are ` vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+alpha hat j+2 hat k , vec c= hat i+2 hat j+alpha hat k` is 15, then find the value of `alpha` if `(alpha>0)dot`

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`