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Foot from $$P(x_0, y_0, z_0)$$ to plane $$ax + by + cz + d = 0$$:
$$ \lambda = -\frac{a x_0 + b y_0 + c z_0 + d}{a^2 + b^2 + c^2} $$
Foot: $$ (x_0 + a\lambda, \quad y_0 + b\lambda, \quad z_0 + c\lambda) $$
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Foot from $$P(x_0, y_0, z_0)$$ to plane $$ax + by + cz + d = 0$$:
$$ \lambda = -\frac{a x_0 + b y_0 + c z_0 + d}{a^2 + b^2 + c^2} $$
Foot: $$ (x_0 + a\lambda, \quad y_0 + b\lambda, \quad z_0 + c\lambda) $$
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