How to find the reflection of a line in a 3D plane

[Saad]

I have a unit test on 3D-Planes coming up! And I was wondering if in 3D, a line and a plane intersect at a single point. How would you determine the equation of the reflection of the line in the plane?
Please try to provide the steps. Thanks!

 

[Chen]

Yes, a plane and a line intersect in one point. Let's say you have the plane:
$$\pi : 7x + 8y + 9z + 10 = 0$$
And the line:
$$\underline{l} = (1, 2, 3) + t(4, 5, 6)$$
You know that the X, Y and Z coordinates of every point on the line are:
$$x = 1 + 4t$$
$$y = 2 + 5t$$
$$z = 3 + 6t$$
Substitute these in the equation of the plane and you will get:
$$7(1 + 4t) + 8(2 + 5t) + 9(3 + 6t) + 10 = 0$$
One unknown - t. Find it and you can find the coordinates of the intersection point.

 

[Chen]

As for finding the reflection, this page explains it quite well:
http://mathforum.org/library/drmath/view/51762.html

 

[Saad]

really appreciate it, this was helpful! thanks!