if `veca=hati+hatj+2hatk, vecb=hati+2hatj+2hatk` and `|vecc|=1`
Such that `[veca xx vecb vecb xx vecc vecc xx veca]` has maximum value, then the value of `|(veca xx vecb) xx vecc|^(2)` is

Options

A. 0
B. 1
C. `4/3`
D. none of these

Answer

A

Explanation

`[veca xx vecbvecb xx veccvecc xx veca]`
`=[vecavecbvecc]^(2) = |vecc. (veca xx vecb)|^(2) cos^(2)theta`
The maximum value of `[vecavecbvecc]` is possible only when `vecc` is parallel to `veca xx vecb`.
`rArr theta=0` or `pi`
Hence, `|(veca xx vecb) xx vecc|^(2) =|veca xx vecb|^(2)|vecc|^(2)sin^(2)theta=0`