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## Main Question or Discussion Point

This is in my multivariable course. How would I find the equation of the line where two planes meet?

I worked out how to find the equation of a plane perpendicular to that line going through a point, Z, (in two planes, Ax + By + Cz +D = 0 and Ex + Fy + Gz + H = 0, take the cross product of (A,B,C) and (E,F,G) and plug the resulting vector into the point-normal form of a plane with the point being Z), but how do I figure out how to find the line itself and how would I find a plane parallel to the line (going through a certain point, Q)? Thanks a lot, guys!

It seems to me, that for the second (plane parallel to a line), I'd need the first (eqn of a line) first. Then I'd find two points on the line and using those three points, I'd find the equation of a plane.

Also, I just thought of something: how would I go about finding the equation of a plane from two vectors. Should I cross them, and then enter either vector as the point in the point-normal form of a plane (i.e. if the vector

I worked out how to find the equation of a plane perpendicular to that line going through a point, Z, (in two planes, Ax + By + Cz +D = 0 and Ex + Fy + Gz + H = 0, take the cross product of (A,B,C) and (E,F,G) and plug the resulting vector into the point-normal form of a plane with the point being Z), but how do I figure out how to find the line itself and how would I find a plane parallel to the line (going through a certain point, Q)? Thanks a lot, guys!

It seems to me, that for the second (plane parallel to a line), I'd need the first (eqn of a line) first. Then I'd find two points on the line and using those three points, I'd find the equation of a plane.

Also, I just thought of something: how would I go about finding the equation of a plane from two vectors. Should I cross them, and then enter either vector as the point in the point-normal form of a plane (i.e. if the vector

**a**is (a1,a2,a3) then could I make (a1,a2,a3) my point?)? Or do I need two vectors and a point not on the vectors?
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