Question

Find the scalar equation of the plane that goes through the line of intersection of the planes 2x+7y+3z+2=0 and x+4y-5z-1=0 that satisfy each equation. (this is two different questions)
a) it has a y intercept of 1
b) it is parallel to the x-axis

Answer 1

If you compute the cross product of the two normal vectors, you're getting a vector that is parallel to the one of the desired line of intersection.

Answer 2

how is that parallel to the x axis? do i have to use the point (1,0,0) anywhere?

Answer 3

I didn't say that it is parallel to the x-axis, I haven't computed the vector product yet, the vector product gives a vector that is perpendicular to the first, and also to the second planes normal vectors. It has the same direction as the line of intersection, so it is a direction vector of that line.

I recommend to first compute the equation of the plane, as requested in the opening paraphrase of your problem. As soon as you have this done, it should be easy to answer a), b)

Answer 4

so they way i solved it, i got it in parametric form and my answers are x=-15-47t
y=-4+13t
and z=t