- #1

Travis Enigma

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- TL;DR Summary
- Vector contained inside the plane.

I have a quick question. If a Vector is contained inside a plane, would the normal of the plane be orthogonal to said vector?

Thank you!

Thank you!

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- Thread starter Travis Enigma
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- #1

Travis Enigma

- 13

- 4

- TL;DR Summary
- Vector contained inside the plane.

I have a quick question. If a Vector is contained inside a plane, would the normal of the plane be orthogonal to said vector?

Thank you!

Thank you!

- #2

- 17,779

- 18,919

Yes. The normal vector of the plane is perpendicular to all vectors in the plane.

- #3

Travis Enigma

- 13

- 4

Okay thank you so much!

- #4

sophiecentaur

Science Advisor

Gold Member

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Does that statement relate to some axiom / definition? Pardon my non-mathematical ignorance but what constrains the normal not to be anywhere in 3D? (I'm thinking Geometry here)Yes. The normal vector of the plane is perpendicular to all vectors in the plane.

- #5

- 17,779

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If you define normality by ##\vec{n} \perp \vec{p}\, \wedge \vec{n}\perp \vec{q} \,,## then we get

$$

0=\lambda \cdot 0+\mu\cdot 0=\lambda \langle \vec{n},\vec{p}\rangle +\mu \langle \vec{n},\vec{q}\rangle=\langle \vec{n},\lambda \vec{p}+\mu\vec{q}\rangle

$$

and again ##\vec{n}\perp \lambda \vec{p}+\mu\vec{q}## for a given pair of coordinates ##(\lambda ,\mu).##

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