The equation of plane passing through the point ( 0 , 7 , - 7 ) and containing the line x + 1 - 3 = y - 3 2 = z + 2 1 is:

Question

The equation of plane passing through the point $(0, 7, - 7)$ and containing the line $\frac{x + 1}{- 3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ is:

Smart Achievers · Accepted Answer

(3)

Ans. $x + y + z = 0$

Explanation:

Equation of plane passing through $(0, 7, - 7)$ is

$a (x - 0) + b (y - 7) + c (z + 7) = 0$ ...(1)

The line passes through $(- 1, 3, - 2)$

Therefore, $a + 4 b - 5 c = 0$ ...(2)

and $- 3 a + 2 b + c = 0$ ...(3)

On solving both equations,

$\frac{a}{14} = \frac{b}{14} = \frac{c}{14} = k$

Therefore, $x + y + z = 0$

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