#### notes

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)