Equation of the plane passing through the line x -1-2- y -1-1- z -3-4 and perpendicular to the plane x -2 y - z -12 is given by ax - by - cz -4-0 then -A- a -8- b -2- c -5B- a -8- b -2- c -5C- a -9- b -2- c -5D- a -9- b -2- c -5

The correct option is D a = 9, b = 2, c = 5The direction ratio of the line is d_1=(2, 1,4) and the D.R. of the given plane is d_2=(1,2,1) The direction rati ...

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Standard XII

Mathematics

Angle between a Plane and a Line

Equation of t...

Question

Equation of the plane passing through the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z - 3}{4}$ and perpendicular to the plane $x + 2 y + z = 12$ is given by $a x + b y + c z + 4 = 0$ then -

a = - 8, b = 2, c = - 5

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a = - 9, b = - 2, c = - 5

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a = 9, b = - 2, c = - 5

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a = 8, b = - 2, c = 5

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Solution

The correct option is C $a = 9, b = - 2, c = - 5$
The direction ratio of the line is $_{1} = (2, - 1, 4)$ and the D.R. of the given plane is $_{2} = (1, 2, 1)$

The direction ration of the required plane is given by $\to n =_{1} \times_{2} = (- 9, 2, 5)$

The point $(1, - 1, 3)$ lies on the plane.

The equation of the required plane is $\to r \cdot \to n = \to a \cdot \to n$

$\Rightarrow 9 x - 2 y - 5 z + 4 = 0$

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Equation of the plane passing through the line x−12=y+1−1=z−34 and perpendicular to the plane x+2y+z=12 is given by ax+by+cz+4=0 then -

Equation of the plane passing through the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z - 3}{4}$ and perpendicular to the plane $x + 2 y + z = 12$ is given by $a x + b y + c z + 4 = 0$ then -