Question

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

Answer 1

Correct Answer - `1`
If image of point `(2, -3, 3)` in the plane `x-2y-z+1=0` is `(a, b, c)`, then
`(a-2)/(1)= (b+3)/(-2)= (c-3)/(-1)= (-2(2-2(-3)-3+1))/((1)^(2)+ (-2)^(2)+ (-1)^(2)) = -2`
Hence, the image is `(0, 1, 5)`
Obviously distance of image of the point from the `z`-axis is 1.