Question

image of the point (1,2,-3) about the plane x+y-z=1

Answer 1

what is the question?

Answer 2

sorry i messed up...the correct normal vector is
<1,1,-1>

line normal to plane going through point (1,2,-3)
x(t) = t+1
y(t) = t+2
z(t) = -t -3

plug these into plane equation to find point where line intersects plane:
(t+1) +(t+2) -(-t-3) = 1

--> t = -5/3

the image is twice distance of point to plane
line hits image point at t = -10/3

image:
\[(-\frac{7}{3},-\frac{4}{3},\frac{1}{3})\]

Answer 3

Thank You!