Question

The equation of the line passing through (1, 2, 3) and parallel to the planes $x - y + 2z = 5$ and $3x + y + z = 6$, is

• A. $\frac{x - 1}{- 3} = \frac{y - 2}{5} = \frac{z - 3}{4}$
• B. $\frac{x - 1}{- 3} = \frac{y - 2}{- 5} = \frac{z - 1}{4}$
• C. $\frac{x - 1}{- 3} = \frac{y - 2}{- 5} = \frac{z - 1}{- 4}$
• D. None of these

Answer 1

Answer: (A)

$\frac{x - 1}{- 3} = \frac{y - 2}{5} = \frac{z - 3}{4}$

Answer 2

$\frac { x - 1 } { l } = \frac { y - 2 } { m } = \frac { z - 3 } { n }$ or $l - m + 2 n = 0$ and

$3 l + m + n = 0$

$\therefore \frac { x - 1 } { - 3 } = \frac { y - 2 } { 5 } = \frac { z - 3 } { 4 }$.