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## Homework Statement

I need to locate the coordinates if a point of intersection x

_{0},y

_{0},z

_{0}of a plane with equation 2x+y-z=0 and a line that is perpendicular to that plane and passes through a point G(2,1,0).

## Homework Equations

andI understand that this is a normal line and a plane so the dot product: {Normal Line}`{P} = 0.

The dot product equals the equation of the plane(right or Is that inaccurate?): {Normal Line}'{P}= a(x-x

_{0})+b(y-y

_{0})+c(z-z

_{0}) = 0

## The Attempt at a Solution

(I have been at this for hours so I have a clump of scratch paper so this is my recent desperate attempt to hack it, im tired and desperate).

My plan: Im given the equation of the plane and a point outside the plane where the line passes through. So essentially I solve for the point of intersection and another point in the plane p(x,y,z) ?

{Normal Line}'{P}= a(x-x

_{0})+b(y-y

_{0})+c(z-z

_{0}) = 0

(a) So, I have a normal line from (2,1,0) to pt. of intersection (x

_{0},y

_{0},z

_{0}) and get the vector eqn of that ?

*Important: 1) When solving is the solution of the normal line and plane a point of intersection just as the solution of two intersecting lines ?*

2)

*Do I necessarily have to solve for another point in the plane perpendicular to the normal line the point of intersection?*I have been wrecking this for some time but nothing adds up in my clumps of scratch paper.

*3) Do I need a parametric representation of the lines?*