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The magnitude of the projection of the v...

The magnitude of the projection of the vector `2hati+3hatj+hatk` on the vector perpendicular to the plane containing the vectors `hati+hatj+hatk" and "hati+2hatj+3hatk`, is

A

`sqrt((3)/(2))`

B

`3sqrt(6)`

C

`(sqrt(3))/(2)`

D

`sqrt(6)`

Text Solution

Verified by Experts

The correct Answer is:
A
Vector perpendicular to plane containing vectors `hati+hatj+hatkand hati+2hatj+3hatk` is parallel to vector
`|{:(hati,hatj,hatk),(1,1,1),(1,2,3):}|=hati-2hatj+hatk`
`:.` Required magnitude of projection is `|((2hati+3hatj+hatk).(hati-2hatj+hatk))/(sqrt(6))|=sqrt((3)/(2))`
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