How have the right to he prove the clues $A=(a_1, a_2, a_3)$, $B=(b_1, b_2, b_3)$, $C=(c_1, c_2, c_3)$, $D=(d_1, d_2, d_3)$ belong to the same plane, as if they belong deserve to then find plane. I know how to prove three offered points belong the exact same plane.

You are watching: Points that lie on the same plane



Take any type of three that the points and determine the equation of the plane. As TonyK said, 3 points always belong to one airplane and, if they execute not every lie in a line, then the identify a unique plane. Once you have the equation the the plane, placed the collaborates of the fourth suggest into the equation to check out if it is satisfied. If the 3 points you made decision do occur to lie on a single line then you room done- any type of fourth point will identify a airplane that all four points lie on.


Hint: analyze by $-A$ so the we have the right to assume $A=(0,0,0)$. Climate points $A,B,C,D$ lied on a aircraft iff vectors $B,C,D$ execute not span whole space, i.e. If $$left| eginarraycccb_1 & b_2 & b_3 \c_1 & c_2 & c_3 \d_1 & d_2 & d_3 endarray ight|=0$$


Thanks for contributing response to jajalger2018.orgematics Stack Exchange!

Please be certain to answer the question. Provide details and share her research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based on opinion; ago them increase with recommendations or an individual experience.

Use jajalger2018.orgJax to format equations. jajalger2018.orgJax reference.

See more: How To Insert A Dotted Line In Word, How To Add A Dotted Line To Any Word Document

To discover more, check out our advice on writing good answers.

article Your answer Discard

By clicking “Post your Answer”, you agree to our terms of service, privacy policy and also cookie policy

Not the answer you're looking for? Browse various other questions tagged geometry or ask your very own question.


site architecture / logo © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.21.40537

her privacy

By clicking “Accept all cookies”, friend agree ridge Exchange deserve to store cookies on your device and disclose information in accordance v our Cookie Policy.