Find a vector of magnitude `6`, which is perpendicular to both the vectors `2hati-hatj+2hatkand4hati-hatj+3hatk`.

Options

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

Answer

D

Explanation

Let `veca=2hati-hatj+2hatkandvecb=4hati-hatj+3hatk`
So, any vector perpendicular to both the vectors ``vecaandvecb` is given by
`vecaxxvecb=|[hati,hatj,hatk],[2,-1,2],[4,-1,3]|
`=hati(-3+2)-hati(6-8)+hatk(-2+4)`
`=-hati+2hatj+2hatk=vecr" "[say]`
A vector of magnitude 6 in the direction of `vecr`
`=(vecr)/(|vecr|).6=(-hati+2hatj+2hatk)/sqrt(1^(2)+2^(2)+2^(2)).6`
`=(-6)/(3)hati+(12)/(3)hatj+(12)/(3)hatk`
`=-2hati+4hatj+4hatk`