Having trouble with a part of a maths question, not sure how to tackle it in an efficient manner
The point A (2, 5, -1) is on the line L, which is perpendicular to the plane with equation $x + y + z - 1 = 0$
The point A is reflected in the plane. Find the coordinates of the image A?
I have already determined the coordinates of the foot of the normal, which is at $(\frac 1 3, \frac {-2}3,\frac 2 3)$
Many thanks for your help!
The normal vector to the plane is
$n=(1,1,1)$
the parametric equations of the line are
$$x=2+t,\;y=5+t,\;z=-1+t$$
the symetric $S(x,y,z)$ is such that the middle is in the plane;
$$\frac{2+2+t}{2}+\frac{5+5+t}{2}+\frac{-1-1+t}{2}-1=0$$
which gives $3t=2-4-10+2=-10$
and $$S(-\frac{4}{3},\frac{5}{3},-\frac{13}{3})$$