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NDA Math Three Dimensional Geometry

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For the next three (3) items that follow :

A plane P passes through the line of intersection of the planes

2x-y+3z=2,x+y-z=1

and the point

(1,0,1)

.

[NDA I 2016]

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Question : 57 of 92

Marks: +1, -0

What is the equation of the plane P?

$2x+5y-2=0$
$5x+2y-5=0$
$x+z-2=0$
$2x-y-2z=0$

Solution:

Eq. of plane through two given planes is :

(2x-y+3z-2)+\lambda(x+y-z-1)=0

∵ It passes through

(1,0,1)

\therefore 3-\lambda=0 \Rightarrow \lambda=3

∴ Eq. of plane is:

5x+2y-5=0

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