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# Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to each of the following planes : $2x+3y-3z=2\: and \: 5x-4y+z=6$

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• $A(x-x_1)+B(y-y_1)+C(z-z_1)=0$
Step 1:
Let the equation of the plane containing the given point $(1,-1,2)$ is
$A(x-x_1)+B(y-y_1)+C(z-z_1)=0$
(i.e) $A(x-1)+B(y+1)+c(z-2)=0$------(1)
Applying the condition of perpendicularly to the plane in equ(1) with the plane
$2x+3y-2z=5$ and $x+2y-3z=8$
We have $2A+3B-2C=0$ and $A+2B-3C=0$
Step 2:
Let us solve three two equations,we get
$A=-5C$
$B=4C$
The required equation is
$-5C(x-1)+4C(y+1)+c(z-2)=0$
$5x-4y-z-7=0$
$5x-4y-z=7$