Question

The equation of the plane passing through the lines $\frac{x - 4}{1} = \frac{y - 3}{1} = \frac{z - 2}{2}$and $\frac{x - 3}{1} = \frac{y - 2}{- 4} = \frac{z}{5}$ is

• A. $11x - y - 3z = 35$
• B. $11x + y - 3z = 35$
• C. $11x - y + 3z = 35$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$a ( x - 4 ) + b ( y - 3 ) + c ( z - 2 ) = 0$

$\therefore a + b + 2 c = 0$ and $a - 4 b + 5 c = 0$

$\frac { a } { 5 + 8 } = \frac { b } { 2 - 5 } = \frac { c } { - 4 - 1 } = k$

$\frac { a } { 13 } = \frac { b } { - 3 } = \frac { c } { - 5 } = k$

Therefore, the required equation of plane is

$- 13 x + 3 y + 5 z + 33 = 0$