# Thread: Parametric line equation and relationship to a plane

1. ## Parametric line equation and relationship to a plane

I have a plane that has an equation of 2x - y + z = 7

My parametric equations for a line L, are

x = - 1 + t

y = 2 + t

z = 1 + 3t

Are these perpendicular to each other, or is line in the plane...
Please someone give me a push in the right direction. Thanks Frostking

2. Originally Posted by Frostking
I have a plane that has an equation of 2x - y + z = 7

My parametric equations for a line L, are

x = - 1 + t

y = 2 + t

z = 1 + 3t

Are these perpendicular to each other, or is line in the plane...
Please someone give me a push in the right direction. Thanks Frostking

So the line is (-1,2,1) + t(1,1,3) ==> since the director vector (1,1,3) is not perpendicular to the given plane (for this the vector would have to be in the same direction as the plane's normal (2,-1,1), the line isn't perpendicular to the plane, but it crosses it: just plug the parametric values of x,y,z into the plane's eq. and find which t solves the equation.

Tonio