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

Options

A. `sqrt(3)/(2)`
B. `sqrt(6)`
C. `3sqrt(6)`
D. `sqrt((3)/(2))`

Answer

D

Explanation

The normal vector to the plane containing the vecotors
`(hati+hatj+hatk)" and "(hati+2hatj+3hatk)` is
`n=(hati+hatj+hatk)xx(hati+2hatj+3hatk)`
`=|{:(hati,hatj,hatk),(1,1,1),(1,2,3):}|`
`=hati(3-2)-hatj(3-1)+hatk(2-1)=hati-2hatj+hatk`
Now, magnitude of the projection of vector `2hati+3hatj+hatk` on normal vector n is
`(|(2hati+3hatj+hatk).n|)/(|n|)=(|(2hati+3hatj+hatk).(hati-2hatj+hatk)|)/(sqrt(1+74+1))`
`=(|2-6+1|)/(sqrt(6))=(3)/(sqrt(6))=sqrt((3)/(2))`units