Question

find the value of a so that th volume fo a so that the valume of the parallelepiped formed by vectors `hati+ahatj+hatk,hatj+ahatkandahati+hatk` becomes minimum.

Answer 1

`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`