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Question
Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0 and the point (2, 2, 1).
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Solution
The equation of any plane through the intersection of the planes, 3x − y + 2z − 4 = 0 and x + y + z − 2 = 0, is
`3x − y + 2z − 4 + alpha`(x + y + z − 2) = 0 where `alpha in R` ....(1)
The plane passes through the point (2, 2, 1). Therefore, this point will satisfy equation (1).
This is the required equation of the plane.
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