Question

Prove that the equation of the plane making intercepts a, b and c on the coordinate axes is of the form x/a + y/b + z/c = 1.

Answer 1

Deriving equation of the plane making intercepts a, b and c on the coordinate axes is of the form $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

    Let the equation of the plane be

                Ax + By + Cz + D = 0     -------------(1)

    (1) passes through (a, 0, 0)

                A(a) + B(0) + C(0) + D = 0

                aA + D = 0

                aA = - D

                A = -D/a

    Similarly,

                 B = -D/b

                 C = -D/c

     Substituting A, B, C in (1)

                $(\frac{-D}{a})x+(\frac{-D}{b})y+\frac{-D}{c})z+D=0$

                 $-\frac{x}{a}-\frac{y}{b}-\frac{z}{c}+1=0$

                   $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$