A variable plane passes through a fixed point D(1, 2, 3). The locus of the foot of the perpendicular drawn from origin to this plane is:

x^{2} + y^{2} + z^{2} - x - 2 y - 3 z = 0

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x^{2} + 2 y^{2} + 3 z^{2} - x - 2 y - 3 z = 0

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x^{2} + 4 y^{2} + 9 z^{2} + x + 2 y + 3 = 0

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x^{2} + y^{2} + z^{2} + x + 2 y + 3 z = 0

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Solution

The correct option is A $x^{2} + y^{2} + z^{2} - x - 2 y - 3 z = 0$
$\begin{matrix} α (x - α) + β (y - β) + γ (z - γ) = 0 α (1 - α) + β (2 - β) + γ (3 - γ) = 0 α + 2 β + 3 γ = α^{2} + β^{2} + γ^{2} α^{2} + β^{2} + γ^{2} - α - 2 β - 3 γ = 0 x^{2} + y^{2} + z^{2} - x - 2 y - 3 z = 0 \end{matrix}$
Option $A$ is correct answer.

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