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Equation of a Plane : Vector Form

Find the equa...

Question

Find the equation of the plane passing through $(1, 1, 1)$ and parallel to the plane $x + 2 y + 3 z - 7 = 0$

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Solution

we can see that
$1^i + 2^j + 3^k$ is the normal vector to plane
$∴$ equation of plane is
$1 (x - 1) + 2 (y - 1) + 3 (x - 1) = 0$
$x + 2 y + 3 z = 6$

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