Vector Calculus: Find Line Perp. to L Through P in 6x-4y+2z=1 Plane

[yoyomath]

Homework Statement

1. Let L (line) be the line given by x = 6 - t, y = 4 + t , z= 4 + t. L intersects the plane 6x - 4y + 2z = 1 at the point P = (6, 4, - 8). Find parametric equations for the line through P which lies in the plane and is perpendicular to L




I don't even know where to start...
I was stuck to this problem for HOURS yesterday

 

[rootX]

What is the direction vector of the line and normal vector of the plane?

Once you have those two vectors, you need to determine what condition the asked line must meet to be in the plane and be perpendicular to the given line.