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Question
Solve the following :
Find the cartesian equation of the plane passing through A(7, 8, 6) and parallel to the plane `bar"r".(6hat"i" + 8hat"j" + 7hat"k")` = 0.
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Solution
The cartesian equation of the plane
`bar"r".(6hat"i" + 8hat"j" + 7hat"k")` = 0 is 6x + 8y + 7z = 0
The required plane is parallel to it
∴ its cartesian equation is
6x + 8y + 7z = p ...(1)
A(7, 8, 6) lies on it and hence satisfies its equation
∴ (6)(7) + (8)(8) + (7)(6) = p
i.e., p = 42 + 64 + 42 = 148.
∴ from (1), the cartesian equation of the required plane is 6x + 8y + 7z = 148.
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