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Question
Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0
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 plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0
Direction ratios of normal vector will be a = 6, b = 8, c = 7.
Equation of a plane in Cartesian form is
a(x − x1) + b(y − y1) + c(z − z1) = 0
∴ 6(x − 7) + 8(y − 8) + 7(z − 6) = 0
∴ 6x − 42 + 8y − 64 + 7z − 42 = 0
∴ 6x + 8y + 7z = 42 + 42 + 64
∴ 6x + 8y + 7z = 148
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