Q. 104.8( 4 Votes )
Show that the plane ax + by + cz + d = 0 divides the line joining the points (x1, y1, z1) and (x2, y2, z2) in the ratio 
.
Answer :
Given: A(x1, y1, z1) and B(x2, y2, z2)
To prove: the ratio in which the line segment AB is divided by the plane ax + by + cz + d = 0 is 
Formula used:
Section Formula:
A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).
The coordinates of C is given by,
Let C(x, y, z) be any point on given plane and C divides AB in ratio k: 1
Therefore, m = k and n = 1
A(x1, y1, z1) and B(x2, y2, z2)
Coordinates of C using section formula:
On comparing:
Since, ax + by + cz + d = 0
The plane divides AB in the ratio 
Hence Provedco
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