Question

The plane passing through the point (-2, -2, 2) and containing the line joining the points (1, 1, 1) and (1, -1, 2) makes intercepts on the coordiantes axes, the sum of whose lengths is

• A. 3
• B. 4
• C. 6
• D. 12

Answer 1

Answer: (D)

12

Answer 2

Equation of any plane passing through (-2, -2, 2) is a (x + 2) + b (y + 2) + c (z - 2) = 0 since it contains the line joining the points (1, 1, 1) and (1, -1, 2), it contains these points as well so that 3a + 3b - c = 0 and 3a + b + 0 = 0 on solving we get $\frac{a}{1} = \frac{b}{-3} = \frac{c}{-6}$ and thus the equation of the plane is $x + 2 - 3 (y + 2) - 6 (z - 2) = 0$ or $x - 3y - 6z + 8 = 0$ or $\frac{x}{-8} + \frac{y}{8/3} + \frac{z}{8/6} = 1$ The required. sum $= 8 + \frac{8}{3} + \frac{8}{6} = 12$.