Question

prove that if plane has intercept a,b,c and is at a distance of p units from the origin then 1/a^a + 1/b^b + 1/c^c = 1/p^p

Answer 1

this is Ur required result in attachment

Answer 2

Hey !!

Let the equation of plane be $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$ -----> (1)

∴ Length of perpendicular from origin to plane (1) is

| $\frac{0}{a} + \frac{0}{b} + \frac{0}{c} - 1$ | / √(1/a)² + (1/b)² + (1/c)²

    = |-1| / √1/a² + 1/b² + 1/c²

    = 1/√1/a² + 1/b² + 1/c²

It is given that

p = 1/√1/a² + 1/b² + 1/c²

=> √1/a² + 1/b² + 1/c² = 1/p

 => 1/a² + 1/b² + 1/c² = 1/p²           ( on squaring both sides )

GOOD LUCK !!