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Question
Find the Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)
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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