I don't understand that hint. the "point normal equation" is the equation of a plane and you want to find a line, not a plane.

Instead, use the fact that the vector equation of a line through and in the direction of vector is .

You already know that , , so you just need to find a vector perpendicular to the plane. And you can do that by taking the cross product of the vectors (from B to A) and (from B to C).

By the way, this is a "Calculus" problem. It doesn't belong in "Linear and Abstract Algebra".