Question

find a equatıon of the plane through p(1,1,1) that intersect th xy plane in the same lıne as does the plane with equatıon 3x+2y-5z=6??

Answer 1

Let z=0 in the equation of your plane, 3x +2y=6, then sub in x=0 to get a point on that line, sub in y=0 to get another point on that line, then together with your orignal point you have 3 points in your desired plane. Make 2 vectors out of your 3 points and take the cross product of them, this will give you the normal vector to your plane. Use the normal vector and your original point to find the equation of the plane