# Equation of a plane

• Sep 2nd 2008, 02:15 PM
mistykz
Equation of a plane
I need to find the plane determined by the two intersecting lines. I've done okay so far with similar problems, but never using two lines like this. Any pointing in the right direction would be greatly appreciated!

L1: x= -1+t y= 2+t z= 1-t -inf< t <inf
L2: x= 1-4s y= 1+2s z=2-2s -inf< s <inf
• Sep 2nd 2008, 02:20 PM
TKHunny
What do you know about the Cross Product?
• Sep 2nd 2008, 02:35 PM
mistykz
If the cross product = 0, the vectors are collinear...
• Sep 2nd 2008, 02:45 PM
Plato
First: Do the lines intersect? If so then find the point.
Second: Find the cross product of the two direction vectors. That is the plane’s normal.
Third: Write the equation of the plane.
• Sep 2nd 2008, 07:07 PM
TKHunny
Quote:

Originally Posted by mistykz
If the cross product = 0, the vectors are collinear...

No, no. That's the dot product, or the inner product. This is a scalar concept. You need the VECTOR concept of a Cross Product.