Find the ratio in which the plane x – 2y + 3z = 5 divides the join of A(3, -5, 4) and B(2, 3, -7). Find the coordinates of the point of intersection of the line and the plane.
Let the plane x – 2y + 3z = 5 divides the join of A(3, -5, 4) and B(2, 3, -7) in ratio k:1.
The point which will come by section formula will be in the plane. Putting that in the plane equation will give the point coordinates. The points are A(3, -5, 4) and B(2, 3, -7).
Using section formula, 
, we get
Putting this point in the plane equation, we get
2k + 3 – 6k + 10 – 21k + 12 = 5k + 5
-25k + 25 = 5k + 5
-30k = -20
the ratio is 2:3. And the point of intersection of the plane and the line is 
1