Vectors Perpendicular to `hati - hatj- hatk` and in the plane of `hati + hatj + hatk and - hati + hatj + hatk` are

Options

A. `hati + hatk`
B. `2hati + hatj + hatk`
C. `3hati+ 2 hatj + hatk`
D. `-4 hati - 2hatj - 2hatk`

Answer

b,d

Explanation

Let `alpha =hati - hatj -hatk , vecbeta = hati + hatj +hatk`
` and vecgmma = -hati +hatj +hatk`
Let requried vector, `veca=xhati + yhatj +zhatj`
then `vecalpha, vecbeta, vecgamma` are coplanar, i.e.
`|{:(x,y,z),(1,1,1),(-1,1,1):}|=0or y=z`
Also `veca and vecalpha` are perpendicular,
` Rightarrow x-y -z =0`
`Rightarrow x = zy`