Find the ratio in

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