Question

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.

Answer 1

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,

\((\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mx_2+nz_1}{m+n})\)

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

k = 2/3

the ratio is 2:3. And the point of intersection of the plane and the line is

(13/5,- 9/5, - 2/5).