Find the Cartesian equation of the plane passing through A(7, 8, 6) and parallel to the plane r.(6i + 8j + 7k) = 0
Find the Cartesian equation of the plane passing through A(7, 8, 6) and parallel to the plane r.(6i + 8j + 7k) = 0
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The cartesian equation of the plane
\(\bar{r}.(6\hat{i} + 8\hat{j} + 7\hat{k}) = 0\) 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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