Vectorial Algebra: Parallel, Perpendicular or Neither?

[sdoyle]

Homework Statement

The line l passes through the point P=(1,-1,1) and has direction vector d=[2,3,-1]. Determine whether l and P are parallel, perpendicular, or neither to 2x+3y-z=1.

Homework Equations

n.x=n.p, also cross product for parallel lines, and dot product for perpendicular.

The Attempt at a Solution

I don't know how to relate the point, P, to the directional vector,d. I am pretty sure that I can do the rest.

 

[Dick]

P isn't related to d, they are independent. 2x+3y-z=1 is a plane. What it's normal vector? Question like this probably don't belong in Physics. I'd put them in a math HW forum.