First slide

Planes in 3D

Question

The foot of the perpendicular from (7, 14, 5) to $2 x + 4 y - z = 2$ is

Moderate

A

$(- 1, 1, 0)$
B

$(1, 2, 8)$
C

$(2, - 1, - 2)$
D

$(1, 2, 3)$

Solution

foot of perpendicular
( $(α, β, γ) \frac{α - x_{1}}{a} = \frac{β - y_{1}}{b} = \frac{γ - z_{1}}{c} = \frac{- (a x_{1} + b y_{1} + c z_{1} + d)}{a^{2} + b^{2} + c^{2}}$

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