“distance from a point to a plane(in 3‐dimensional space)”的概念、定义、翻译、参考文献-科学参考

distance from a point to a plane(in 3‐dimensional space)

Mathematics

The distance from the point P to the plane p is the shortest distance between P and a point in p, and is equal to |PN|, where N is the point in p such that the line PN is normal to p. If P has coordinates (x₁, y₁, z₁) and p has equation ax + by + cz + d = 0, the distance from P to p is equal to

$\frac{| a x_{1} + b y_{1} + c z_{1} + d |}{\sqrt{a^{2} + b^{2} + c^{2}}}$

where |ax₁ + by₁ + cz₁ + d| is the absolute value of ax₁ + by₁ + cz₁ + d.

单词	distance from a point to a plane(in 3‐dimensional space)
释义	distance from a point to a plane(in 3‐dimensional space) Mathematics The distance from the point P to the plane p is the shortest distance between P and a point in p, and is equal to \|PN\|, where N is the point in p such that the line PN is normal to p. If P has coordinates (x₁, y₁, z₁) and p has equation ax + by + cz + d = 0, the distance from P to p is equal to $\frac{\| a x_{1} + b y_{1} + c z_{1} + d \|}{\sqrt{a^{2} + b^{2} + c^{2}}}$ where \|ax₁ + by₁ + cz₁ + d\| is the absolute value of ax₁ + by₁ + cz₁ + d.
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