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

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.

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RELATED QUESTIONS :

Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers