# Intersecting Lines in a Plane

• March 31st 2009, 01:25 PM
square
Intersecting Lines in a Plane
Equation of plane: r= (-3,5,6) + s[-1,1,2] + v[2,1,-3]. I need the equation of 2 intersecting lines that lie on this plane. I know I can use s[-1,1,2], but I need to find another vector that is perpendicular to s[-1,1,2]. How can I find the intersecting vector?
• March 31st 2009, 10:30 PM
earboth
Quote:

Originally Posted by square
Equation of plane: r= (-3,5,6) + s[-1,1,2] + v[2,1,-3]. I need the equation of 2 intersecting lines that lie on this plane. I know I can use s[-1,1,2], but I need to find another vector that is perpendicular to s[-1,1,2]. How can I find the intersecting vector?

The vector you are looking for is

$\vec v = (-1,1,2) \times \underbrace{\left((-1,1,2) \times (2,1,-3) \right)}_{\text{normal to plane}} = (-5,-1,4)$