- #1
Hellken
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Homework Statement
I need to locate the coordinates if a point of intersection x0,y0,z0 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-x0)+b(y-y0)+c(z-z0) = 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, I am tired and desperate).
My plan: I am 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-x0)+b(y-y0)+c(z-z0) = 0
(a) So, I have a normal line from (2,1,0) to pt. of intersection (x0,y0,z0) 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?