The reflection of the point `veca` in the plane `vecr.vecn=q` is (A) `veca+ (vecq-veca.vecn)/(|vecn|` (B) `veca+2((vecq-veca.vecn)/(|vecn|^2))vecn` (C) `veca+(2(vecq+veca.vecn))/(|vecn|)` (D) none of these

Options

A. `veca+((vecq-veca.vecn))/(|vecn|)`
B. `veca+2(((vecq-veca.vecn))/(|vecn|^(2)))vecn`
C. `veca+(2(vecq-veca.vecn))/(|vecn|)vecn`
D. none of these

Answer

b

Explanation

Given plane is `vecr.vecn=q`
Let the image of `A(veca)` in the plane be `B(vecb)`.

Equation of AC is `vecr=veca+lamdavecn`
(`because` AC is normal to the plane) (ii)
Solving (i) and (ii), we get
`(veca+lamdavecn).vecn=q`
or `lamda=(q-veca.vecn)/(|vecn|^(2)).vecn`
But `vec(OC)=(veca+vecb)/(2)`
`becauseveca+((q-veca.vecn)vecn)/(|vecn|^(2))=(veca+vecb)/(2)`
or `vecb=veca+2((q-veca.vecn)/(|vecn|^(2)))`