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