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Question
Find the Cartesian equation of the plane passing through A(7, 8, 6) and parallel to the XY plane.
Solution
The Cartesian equation of the plane passing through (x1, y1, z1), the direction ratios of whose normal are a, b, c, is
a(x – x1) + b(y – y1) + c(z – z1) = 0
The required plane is parallel to XY-plane.
∴ it is perpendicular to Z-axis i.e. Z-axis is normal to the plane. Z-axis has direction ratios 0, 0, 1.
The plane passes through (7, 8, 6).
∴ the cartesian equation of the required plane is
0(x – 7) + 0(y – 8) + 1(z – 6) = 0
i.e. z = 6.
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