Question

The three planes 4y + 6z = 5 ; 2x + 3y + 5z = 5;

6x + 5y + 9z = 10

• A. meet in a point
• B. have a line in common
• C. form a triangular prism
• D. none of these

Answer 1

Answer: (B)

have a line in common

Answer 2

If d.c.’s of line of intersection of planes 4y + 6z = 5 &

2x + 3y + 5z = 5 are l, m, n

\ 0 + 4m + 6n = 0, 2l + 3m + 5n = 0

Ž $\frac{l}{1}$ = $\frac{m}{6}$ = $\frac{n}{- 4}$ = $\frac{1}{\sqrt{53}}$

Ž l = $\frac{1}{\sqrt{53}}$, m = $\frac{6}{\sqrt{53}}$, n = $\frac{- 4}{\sqrt{53}}$

also 6 $\left( \frac{1}{\sqrt{53}} \right)$ + 5 $\left( \frac{6}{\sqrt{53}} \right)$ + 9 $\left( - \frac{4}{\sqrt{53}} \right)$ = 0

i.e., line of intersection in ^ to normal of third plane Hence plane. Hence three planes have a line in common.