The image of the point with position vector `hat(i)+3hat(k)` in the plane `r*(hat(i)+hat(j)+hat(k))=1` is

Options

A. `hat(i)+2hat(j)+hat(k)`
B. `hat(i)+2hat(j)-hat(k)`
C. `-hat(i)-2hat(j)+hat(k)`
D. `hat(i)-2hat(j)+hat(k)`

Answer

C

Explanation

Here, the point is (1,0,3) and equation of plane is `x+y+z=1`.
Let `alpha,beta and gamma` be the image of plane.
Then `(alpha-1)/(1)=(beta-0)/(1)=(gamma-3)/(1)=(-2(1+0+3-1))/(1^(2)+1^(2)+1^(2))`
`rArr" "(alpha-1)/(1)=(beta)/(1)=(gamma-3)/(1)=(-6)/(3)rArralpha=-1,beta=-2,gamma=1`
Hence, the image is `(-hat(i)-2hat(j)+hat(k))`.