Question

Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b' ,c' from the origin, then

(a) 1/a² + 1/b² + 1/c² + 1/a'² + 1/b'² + 1/c'² = 0

(b) 1/a² + 1/b² - 1/c² + 1/a'² + 1/b'² - 1/c'² = 0

(c) 1/a² - 1/b² - 1/c² + 1/a'² - 1/b'² - 1/c'² = 0

(d) 1/a² + 1/b² + 1/c² - 1/a'² - 1/b'² - 1/c'² = 0

Answer 1

Correct option (d) 1/a² + 1/b² + 1/c² - 1/a'² - 1/b'² - 1/c'² = 0

Explanation:

Consider OY, OY, OZ and Ox, Oy, Oz are two systems of rectangular axes.

Let their corresponding equations of plane be

Length of perpendicular from origin to Eqs. (i) and (ii) must be same,