A vector perpendicular to `(hat(i)+hat(j)+hat(k))` and `(hat(i)-hat(j)-hat(k))` is :-

Options

A. `hat(i)+hat(j)+hat(k)`
B. `hat(i)+hat(k)`
C. `-1hat(i)+hat(j)+hat(k)`
D. `hat(j)+hat(k)-2hat(i)`

Answer

C

Explanation

Let the vector be `(xhat(i)+yhat(j)+xhat(k))`
`(xhat(i)+yhat(j)+ zhat(k)).(hat(i)-hat(j)-hat(k))=0`
`x+y-z=0" " `........(1)
`(xhat(i)+yhat(j)+zhat(k)).(hat(i)-hat(j)-hat(k))=0`
`x-y-z=0 " "`.......(2)
Subtracting (1)& (2)
`rArr y=0`
`& " " x=z`
Hence possible vector is Ans.B