Q. 104.8( 4 Votes )

# Show that the plane ax + by + cz + d = 0 divides the line joining the points (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) in the ratio .

Answer :

**Given:** A(x_{1}, y_{1}, z_{1}) and B(x_{2}, y_{2}, z_{2})

**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(x_{1}, y_{1}, z_{1}) and B(x_{2}, y_{2}, z_{2})

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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