Relative to a fixed origin, the line has the equation:
The point lies on and is such that is perpendicular to .
EDIT: The question is - Find the coordinates of .
Let this point be and
Since C is on the line, we can see that:
Since , then :
Convert a,b, c into terms of lambda and solve for it. Then, plug it in back to the equation of your line to get which should correspond to your point as it originates form the origin.