If `veca,vecb` and `vecc` are three non-coplanar vectors then the length of projection of vector `veca` in the plane of the vectors `vecb` and `vecc` may be given by

Options

A. `(|veca.(vecbxxvecc)|)/(|vecbxxvecc|)`
B. `|(vecaxx(vecbxxvecc)|)/(|vecbxxvecc|)`
C. `([(veca,vecb,vecc)])/(vecb.vecc)`
D. none of these

Answer

B

Explanation

A vector normal to the plane containing `vecb` and `vecc` is `vecn=vecbxxvec`
We have
`BN=` Projection of `veca` on `vecn=veca.hatn`
`:.` Projection of `veca` on the plane containing `vecb` and `vecc`
`=LM=AN=sqrt(AB^(2)-BN^(2))`
`=sqrt(|veca|^(2)-(veca.hatn)^(2))=sqrt(|veca|^(2)|hatn|^(2)(veca.hatn)^(2))`
`=sqrt(|vecaxxhatn|^(2))=|vecaxxhatn|=(|vecaxx(vecbxxvecc)|)/(|vecbxxvecc|)`