Write the ratio i

We know that, the ratio in which the plane Ax + By + Cz + D=0 (where ) divides the line segment joining (x₁, y₁, z₁) and (x₂, y₂, z₂) then is given as,

Here, the equation of the given plane is, 4x + 5y–3z=8 i.e. 4x + 5y–3z - 8=0 and the co - ordinates of the two points are (–2, 1, 5) and (3, 3, 2).

Comparing with the general formula, we get,

A=4, B=5, C= - 3, D= - 8, x₁= - 2, y₁=1, z₁=5and x₂=3, y₂=3 and z₂=2.

So, the required ratio is

Hence, the plane 4x + 5y–3z=8 divides the line segment joining points (–2, 1, 5) and (3, 3, 2) in 2:1 ratio.