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The number of unit vectors perpendicular...

The number of unit vectors perpendicular to the plane of vectors `veca=2hati-6hat j-3hatk` and `vecb=4hati+3hatj-hatk` is/are

A

` 1/ sqrt26 ( 4hati = 3hatj -hatk)`

B

`1/7 (2hati -6hatj -3hatk)`

C

` 1/7 (3hati + 2hatj + 6hatk)`

D

`1/7 (2hati -3hatj -6hatk)`

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
`vecaxxvecb=|{:(hati,hatj,hatk),(2,-6,-3),(4,3,-1):}|=5 (3hati-2hatj+6hatk)`
`|veca xx vecb|=5 sqrt( 9 + 4+36) =35`
Hence, required unit vector `vecn` is given by
` hatn = 4/35 ( 3hati -2hatj + 6hatk) = 1/7( 3hati -2hatj +6hatk)`
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