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Question
Find the Cartesian equation of the plane passing through A(7, 8, 6)and parallel to XY plane
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Solution
The plane passes through the point A(7, 8, 6).
∴ x1 = 7, y1 = 8, z1 = 6.
Since the required plane is parallel to the XY plane, direction ratios of normal vector will be a = 0, b = 0, c = 1(Z-axis).
Equation of a plane in Cartesian form is
a(x − x1) + b(y − y1) + c(z − z1) = 0
∴ 0(x − 7) + 0(y − 8) + 1(z − 6) = 0
∴ z − 6 = 0
∴ z = 6
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