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A unit vector perpendicular to the plane...

A unit vector perpendicular to the plane of ` veca = 2hati -6hatj -3hatk and vecb = 4hati +3hatj-hatk ` is

A

`(4hati-3hatj-hatk)/(sqrt(26))`

B

`(2hati-6hatj-3hatk)/(7)`

C

`(3hati-2hatj+6hatk)/(7)`

D

`(2hati-3hatj-6hatk)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `a=2hati-6hatj-3hatk`
and `b=4hati+3hatj-hatk`
`thereforeaxxb=[(hati,hatj,hatk),(2,-6,-3),(4,3,-1)]`
`=15hati-10hatj+30hatk`
`|axxb|=sqrt((15)^(2)+(-10)^(2)+(30)^(2))`
`=sqrt(1225)=35`
Hence, required vector`=(axxb)/(|axxb|)`
`=(15hati-10hatj+30hatk)/(35)=(3hati-2hatj+6hatk)/(7)`
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