Find the image of the point `(1,3,4)` in the plane `2x-y+z+3=0.`

Options

A. `(3,5,2)`
B. `(-3,5,2)`
C. `(3,5,-2)`
D. `(3,-5,2)`

Answer

B

Explanation

Let `(alpha, beta, gamma)` be the image of the point `(1,3,4)` in the plane `2x-y+z+3=0` then
`(alpha-1)/2=(beta-3)/(-1)=(gamma-4)/1=-(2(2xx1-3xx1+4xx1+3))/(2^(2)+(-1)^(2)+1^(2))`
`implies(alpha-1)/2=(beta-3)/(-1)=(gamma-4)/1=-2impliesalpha=-3,beta=5,gamma=2`
Hence the image has the coordinates `(-3,5,2)`