A vector of magnitude `sqrt2` coplanar with the vectors `veca=hati+hatj+2hatk and vecb = hati + hatj + hatk,` and perpendicular to the vector `vecc = hati + hatj +hatk` is

Options

A. `-hatj+hatk`
B. `hati and hatk`
C. `hati - hatk`
D. `hati- hatj`

Answer

a

Explanation

A vector coplanar with `veca and vecb` and perpendicular to `vecc is lambda (veca xx vecb) xx vecc)`
but `lambda(veca xx vecb xx vecc) = lambda [ (veca . Vecc) vecb- (vecb .vecc) veca]`
` lambda [ 4vecb - 4 veca]`
`4 lambda [ vecj -hatk]`
Hence, the required vector vector, is `hatj - hatk or -hatj + hatk`