Determine if lines are parallel, intersecting, or skew

Determine if two 3D lines are parallel, intersecting, or skew

[@mikeharmer7720]

This was very helpful, straight forward and plane english. Thank you

[@MrShortDictionary]

not sure if that's a pun or just a typo but either way it made me smile

[@prestonsparks3794]

+Mike Harmer plain* lol

[@آلَحًلَآوُيّة-ق9غ]

Thank you very much, doctor, for this beautiful and valuable information. Thank you from the bottom of my heart. I love you so much. 🌹❤I am Noor from Iraq,🇮🇶 a medical equipment engineer, second stage. 🥰

[@MitchInBeanie]

This was extremely helpful, thank you.

[@dillonbenson7741]

how do we determine the point of intersection, after finding t & s?

[@catboat863]

Literally no one can answer this question, it's so annoying

[@ConceptualCalculus]

Take the values of s and t that you have found, and put them into the original equations. Putting t into the first equation should give you the same values of x, y, and z that you get from putting s into the second equation. That is your point of intersection.

[@wokaroni]

@@ConceptualCalculus thank you, very helpful

[@rakshaaiyappan8193]

thanks but what about skew

[@unknown-gy8jz]

when the line not parallel and intersect then automatically the line is skew

[@dwzheng]

very helpful! thank you

[@ConceptualCalculus]

In the first example, the lines are *not* parallel. They are coincident, meaning that they are two different ways of describing the exact same line.

[@aidanvega9778]

no

[@ConceptualCalculus]

@@aidanvega9778 ???

[@Kj-mf6sy]

@@ConceptualCalculus it is parallel.

[@ConceptualCalculus]

@@Kj-mf6sy At t = 1, the first line passes through r1(1) = + 1 = .
At t = 0, the second line passes through r2(0) = + 0 =
Parallel lines never intersect. If the lines were parallel, they would not both pass through the same point, as these lines do. They are coincident lines. That means r1 and r2 are two different ways of describing the same line.

[@cameodamaneo]

Could you just do a simultaneous equation for t and 2 for y and z instead of a system of equations?

[@mythologyandhistory9995]

Very helpful 👍

[@zertbrown4642]

thank you, you are the best!

[@starohaggai]

Awesome video

[@philipi85]

Thank you. Great video.

[@shrawanipal]

if they are parallel and they intersect, it means they are co-incident right?

[@ConceptualCalculus]

Yes.

[@IronElephantProductions]

thank you so much

[@nidhishgautam9043]

Thanks a lot.

[@partydenmer6969]

Saved my ass... my final exam is tmrw fuckkkkk

[@bismabisma9892]

What about skew lines??

[@RadhaRambles]

What are skew lines? Lines that are not parallel or intersecting (or coplanar).