What is the point-normal form of the equation of a plane?

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What is the point-normal form of the equation of a plane?

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Answer 1 · 2016-11-10T15:20:25

See below.

Explanation:

Given a fixed point

$p_{0} = (x_{0}, y_{0}, z_{0})$ $p_0=(x_0,y_0,z_0)$

an a generic point

$p = (x, y, z)$ $p = (x,y,z)$

and a non null vector

$\to n = (n_{x}, n_{y}, n_{z})$ $vec n = (n_x,n_y,n_z)$

the formulation $⟨ p - p_{0}, \to n ⟩ = 0$ $<< p-p_0, vec n >> = 0$ with $⟨ \cdot, \cdot ⟩$ $<< cdot, cdot >>$ representing scalar product, indicates the set of points including $p_{0}$ $p_0$ that are orthogonal to the vector $\to n$ $vec n$ .

We have also the long version as

$(x - x_{0}) n_{x} + (y - y_{0}) n_{y} + (z - z_{0}) n_{z} = 0$ $(x-x_0)n_x+(y-y_0)n_y+(z-z_0)n_z=0$

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What is the point-normal form of the equation of a plane?

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