parametric equation of line.

I have a normal vector (2,-2,0) of the a plane and a point on a line orthogonal to the plane, (4,0,1). So my goal is to try and find the parametric description of this line.

now to do that I need a vector v, but how can I find this vector with the given info?

the parametric representation is given by p + tv where p is a point and v is a vector. I need another point on this line to find the vector. Since this line is orthogonal to the plane I know that this vector should be parallel to the normal vector of the plane. But im having difficulty trying to find another point on this line.

Re: parametric equation of line.

maybe i'm missing something, here....why doesn't (4,0,1) + t(2,-2,0) work?

Re: parametric equation of line.

Well the line and the normal vector to the plane are parallel, but how do we know that the normal vector lies on the line?

I'm a bit confused myself. How can you just say (4,0,1) + t(2,-2,0) is the equation?

Re: parametric equation of line.

Re: parametric equation of line.

the normal vector usually doesn't lie on the line going through a given point, it's just parallel to the line (there's a whole plane's worth of such lines, like a bundle of straws all lined up together).

but if we specify a point (any point) then we know which parallel line. "orthogonal to" and "normal" have almost the same meaning (usually, a normal vector is associated with some particular point in the plane). thus, every orthogonal vector to a plane (it's line direction) is parallel to a normal vector to a plane.