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
- ax1+ by1+ cz1+ d / ax2 + by2 + cz2 + d .
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Ratio will be same as the ratio of the perpendiculars drawn from these points on the plane. The following figure explains this
Length of perpendicular drawn, in units, from (x1, y1, z1) to the plane
Length of perpendicular drawn, in units, from (x2, y2, z2) to the plane
Also, the above two values inside the modulus brackets are of opposite signs as the points are on opposite sides of the plane.
Hence ratio =