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Question

Find the equation of the plane that contains the point (1, −1, 2) and is perpendicular to each of the planes 2x + 3y − 2z = 5 and x + 2y − 3z = 8.

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Solution

The equation of any plane passing through (1, -1, 2) isa x-1+b y+1+c z-2=0 ... 1It is given that (1) is perpendicular to the plane 2x+3y-2z=5. So,2a+3b-2c=0... 2It is given that (1) is perpendicular to the plane x+2y-3z=8. So,a+2b-3c=0 ... 3Solving (1), (2) and (3), we getx-1y+1z-223-212-3=0-5 x-1+4 y+1+1 z-2=05x-4y-z=7

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