Find the three dimensional line that goes through point p and is perpendicular to a plane

Question

I am given the point $P(1,0,6)$ and I need to find a line that goes through $P$ and is also perpendicular to $x+3y+z=5$. Background info: I've gotten the help I needed now but when I started I was unaware about the method to find a vector perpendicular to the plane and how to find a line equation which uses that vector and goes through the point P.

Answer 1

Hint: the normal vector to the plane $ax+by+cz=d$ is $(a,b,c)$. To find a line you only need a point and a direction. Now you finish it.