Which one of the following vectors is a magnitude 6 and perpendicular to both `a=2hati+2hatj+hatk and b=hati-2hatj+2hatk`?

Options

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

Answer

D

Explanation

Now , `axxb=|{:(hat(i),hat(j),hat(k)),(2,2,1),(1,-2,2):}|=hat(i)(4+2)-hat(j)(4-1)+hat(k)(-4-2)`
`6hat(i)-3hat(j)-6hat(k)`
`|axxb|=sqrt(36+9+36)=sqrt(81)=9`
`therefore` Requried vectors are `+-6|(axxb)/(|axxb||)|=+-(6)/(9)(6hat(i)-3hat(j)-6hat(k))=+-2(2hat(i)-hat(j)-2hat(k))`