(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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).

2. Relevant equationsand

I 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

3. 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?

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# Homework Help: Point of intersection of a line and plane. No points in plane given. Wheres SUPERMAN?

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