The value of a so thast the volume of parallelpiped formed by vectors `hati+ahatj+hatk, hatj+ahatk, ahati+hatk` becomes minimum is (A) `sqrt93)` (B) 2 (C) `1/sqrt(3)` (D) 3

Explanation

`V=|{:(1,a,1),(0,1,a),(a,0,1):}|=1-a+a^(3)`
`Rightarrow" " (dV)/(da)=3a^(2)-1`
V is minimum at a `=1/sqrt3`