Condition for two spheres x^2 + y^2 + z^2 + 2g1 x + 2f1 y + 2h1 z + c1 = 0 and x^2 + y^2 + z^2 + 2g2 x + 2f2 y + 2h2 z +...

Type: MCQ • Marks: 1

Condition for two spheres x^2 + y^2 + z^2 + 2g1 x + 2f1 y + 2h1 z + c1 = 0 and x^2 + y^2 + z^2 + 2g2 x + 2f2 y + 2h2 z + c2 = 0 to be orthogonal is:

A. g1 g2 + f1 f2 + h1 h2 = 0

B. g1 g2 + f1 f2 + h1 h2 = c1 + c2

C. 2g1 g2 + 2f1 f2 + 2h1 h2 = c1 + c2

D. 2g1 g2 + 2f1 f2 + 2h1 h2 = c1 c2

Explanation

The condition of orthogonality for two spheres is 2 g1 g2 + 2 f1 f2 + 2 h1 h2 = c1 + c2.

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