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Equation of a Plane Parallel to a Given Plane

The vector eq...

Question

The vector equation of the plane through the point $(2, 1, - 1)$ and parallel to the plane $r \cdot (i + 3 j - k) = 0$ is

r \cdot (i + 9 j + 11 k) = 6

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r \cdot (i - 9 j + 11 k) = 4

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r \cdot (i + 3 j - k) = 6

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r \cdot (i + 3 j - k) = 4

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r \cdot (i + 3 j + k) = 6

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Solution

The correct option is C $r \cdot (i + 3 j - k) = 6$
Given equation of plane is
$r \cdot (i + 3 j - k) = 0$
Therefore, required equation of plane passing through $(2, 1, - 1)$ and parallel to the given plane is
$[r - (2 i + j - k) \cdot (i + 3 j - k) = 0$
$\Rightarrow r \cdot (i + 3 j - k - (2 + 3 + 1) = 0$
$\Rightarrow r \cdot (i + 3 j - k) = 6$

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