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Equation of a Plane : Normal Form

The equation ...

Question

The equation of the plane passing through $(a, b, c)$ and parallel to the plane $r . (^i +^j +^k) = 2$ is,

x + y + z = 1

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a x + b y + c z = 1

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x + y + z = a + b + c

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None of these

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Solution

The correct option is A $x + y + z = a + b + c$
Let any point on the plane be $(x, y, z)$ then,
$1 (x - a) + 1 (y - b) + 1 (z - c) = 0 ⟹ x + y + z = a + b + c$

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