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Question
Find the Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)
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Solution
The Cartesian equation of the plane passing the points (3, 2, 1) = (x1, y1, z1) and (1, 3, 1) = (x2, y2, z2) is
`(x - x_1)/(x_2 - x_1) = ("y" - "y"_1)/("y"_2 - "y"_1) = ("z" - "z"_1)/("z"_2 - "z"_1)`
∴ The Cartesian equation of plane is
`(x - 3)/(1 - 3) = ("y" - 2)/(3 - 2) = ("z" - 1)/(1 - 1)`
i.e., `(x - 3)/(-2) = ("y" - 2)/1`; z = 1
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