A vector of magnitude `sqrt2` coplanar with `hati+hatj+2hati` and `hati+2hatj+hatk` and perpendicular to `hati+hatj+hatk` is

Options

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

Answer

A

Explanation

A vector coplanar with `hat(i)+hat(j)+2hat(k)` and `hat(i)+2hat(j)+hat(k)` is
`hat(i)+hat(j)+2hat(k)+lambda(hat(i)+2hat(j)+hat(k))=(1+lambda)hat(i)+(1+2 lambda)hat(j)+(2+lambda)hat(k)`
it is perpendicular to `hat(i)+hat(j)+hat(k)`
`:. 1+lambda+1+2 lambda+2+lambda =0" "[ :' a.b=0]`
`implies lambda=-1`
`:.` Required vector is `-hat(j)-hat(k)`.