Finding the point of intersection of straight through the points A (3,-5,2) and B (11,-3,6) with the straight (r): (x,y,z) = (5,-3,2) + t (4,-2,4).
First find the direction vector of your line, i.e. .
Now, can simply the vector from the origin to the point A (or B, doesn't matter as long as it's on the line). So, our line is:
Now to see where lines s and r intersect, we set the them equal to each other, i.e. .