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Plane - Intercept Form of the Equation of a Plane

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the equation of a plane in terms of the intercepts made by the plane on the coordinate axes.  Let the equation of the plane be 
Ax + By +Cz +D = 0      (D ≠ 0)                      ... (1) 
Let the plane make intercepts a, b, c on x, y and z axes, respectively in following fig. 

Hence, the plane meets x, y and z-axes at (a, 0, 0), (0, b, 0), (0, 0, c), respectively.
Therefore  Aa + D = 0  or A = `(-D)/a`
Bb + D = 0   or B = `(-D)/b`
Cc +D = 0  or C = `(-D)/c`
Substituting these values in the equation (1) of the plane and simplifying, we get 
`x/a + y/b +z/ c = 1`                    ...(1)

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Shaalaa.com | 3 Dimensional Geometry part 23 (Example :- Plane through intersecting plans)

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3 Dimensional Geometry part 23 (Example :- Plane through intersecting plans) [00:08:09]
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