Question

Find the equation of the line that passes through the point A(3,-1,2) and is parallel to the intersection line of the two planes x+y+3z -10=0 and 6x-2y+z-10=0. (hint: recall that you need a direction vector to find the equation of the line.)

Answer 1

Any plane passing thru intersection of given planes is :

\(x+y+3z -10 + k(6x-2y+z-10) = 0\)

Answer 2

since you know a point on the plane,
plug it in and find \(k\) value