Question

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is (1/2). Then, the plane passes through the point 

A. (0, 0, 0) 

B. (1, 1, 1)

C. \((\frac{1}2,\frac{1}2,\frac{1}2)\)

D. (2, 2, 2)

Answer 1

Given: Variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is (1/2) 

Formula Used: Equation of a plane is

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

Explanation: 

Let the intercepts made by the plane on the co-ordinate axes be a, b and c.

⇒ \(\frac{1}a\) + \(\frac{1}b\) + \(\frac{1}c\) = \(\frac{1}2\)

Let the equation of the plane be

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

On solving for each of the given options, 

(0, 0, 0) ⇒ LHS ≠ RHS 

(1, 1, 1) ⇒ LHS ≠ RHS

Therefore, plane passes through the point (2, 2, 2)