The length of the perpendicular from the origin to the plane passing through the points `veca` and containing the line `vecr = vecb + lambda vecc` is

Options

A. `([vecavecbvecc])/(|vecaxxvecb+vecbxxvecc+veccxxveca|)`
B. `([vecavecbvecc])/(|vecaxxvecb+vecbxxvecc|)`
C. `([vecavecbvecc])/(|vecbxxvecc+veccxxveca|)`
D. `([vecavecbvecc])/(|veccxxveca+vecaxxvecb|)`

Answer

c

Explanation

The given plane passes through `veca` and is parallel to the vectors `vecb-vecaandvecc`. So it is normal to
`(vecb-veca)xxvecc`. Henec, its equation is `(vecr-veca).((vecb-veca)xxvecc)=0`
or `vecr.(vecbxxvecc+veccxxveca)=[vecavecbvecc]`
The length of the perpendicular from the origin to this plane is
`[vecavecbvecc]/(|vecbxxvecc+veccxxveca|)`