Q. 12

Find the equation of the plane passing through the point A(-1, -1, 2) and perpendicular to each of the planes 3x + 2y - 3z = 1 and 5x – 4y + z = 5.

Answer :

Applying the condition of perpendicularity between planes


Where A, B, C are direction ratios of plane and A1, B1, C1 are of another plane.


(1)


(2)


And plane passes through (-1,-1,2),


A(x + 1) + B(y + 1) + C(z-2)=0 (3)


On solving equation (1) and (2)



Putting values in equation (3)



B(5x + 5 + 9y + 9 + 11z-22)=0


5x + 9y + 11z-8=0


So, required equation of plane is 5x + 9y + 11z=8.


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