Thread: Another whether a line is parallel to a plane?

How can you tell whether the line x = x0 + tv in R3 is parallel to the plane x = x0 + t1v1 + t2v2 ?

Hey Civy71.

Hint: If a line lies on a plane then the line will be perpendicular to the plane normal.

Originally Posted by Civy71

How can you tell whether the line in R3 is parallel to the plane ?

Surely both line and plane have in common.

Question is

yes, it equals 0

Originally Posted by Civy71

yes, it equals 0

Well then, a line with direction vector is parallel to a plane with normal if and only if .

Here's another way to view the solution, purely algebraic.

Originally Posted by Civy71

How can you tell whether the line x = x0 + tv in R3 is parallel to the plane x = x0 + t1v1 + t2v2 ?

v.v1Xv2 = 0. Same as det |v,v1,v2 | = 0 , ie v, v1 and v2 are linearly dependent.

EDIT: v is a vector in the direction of the line. v1 and v2 are vectors in the plane.