The image of the point (1,2,3) by the plane, x+y+z+3=0 is

Options

A. `(-5,4,-3)`
B. `(-5,-4,-3)`
C. `(5,-4,3)`
D. `(5,4,3)`

Answer

B

Explanation

The image (x,y,z) of the point (1,2,3) by the plane
`x+y+z+3=0" is "(x-1)/(1)=(y-2)/(1)=(z-3)/(1)" is "`
`=-2*((1xx1+1xx2+1xx3=3))/(1^(2)+1^(2)+1^(2))`
`rArr" "(x-1)/(1)=(y-2)/(1)=(z-3)/(1)=-6`
`rArr" "x=-5,y=-4,z=-3`
Hence, required image point is (-5,-4,-3).