Intersection of Two Lines in 3D Space | Intersecting Lines

Learn how to find the point of intersection of two 3D lines. Starting from 2 lines equation, written in vector form, we write them in their parametric form and solve three equations, with two unknowns simultaneously to find if and where the two lines intersect. We also see how to distinguish whether the two lines intersect or are skew. The worked example is detailed and all the steps are shown.

[@RadfordMathematics]

Can you help me make more vidoes🤚? “buy me a coffee” ? to help 😊: buymeacoffee.com/radfordmath

[@shayson1357]

OMG 10 different videos with garbage explanation until I saw this, you ARE GODLIKE !

[@RadfordMathematics]

Thanks for such kind words 😊 I’m really glad it helped! You may find the one I recently made on skew lines in 3D space useful as well. In case it’s of interest, here’s the link: kzbin.info/www/bejne/amiolKyprpd_pNU Take good care ✌️

[@Shodan159]

Thank you very much. Very clear explanation. Made the concepts and processes easy to understand.

[@RadfordMathematics]

Thanks for your comment Ethan! I really appreciate it! Truly glad this video helped 😊 Take good care ✌️

[@TJATMAJA]

Excellent explanation, this was very helpful. Thank you.

[@RadfordMathematics]

Thanks for taking the time to comment Liam and for your kind words, I really appreciate it 😊 If you’re studying that topic you may find my tutorial on skew lines useful. In case it’s of interest here’s the link: kzbin.info/www/bejne/amiolKyprpd_pNU In any case, take good care ✌️

[@dhinastea]

Very well presented and the explanations are really clear!! Thank you

[@RadfordMathematics]

Thanks for your comment 😊 Really glad it helped ✌️

[@nonamegivin3884]

thanks so much I cant belive something so simple took me so long to figure out.

[@RadfordMathematics]

Thanks for your comment 😊 I’m really glad this helped figure it out!!

[@muhammadusamajamil2685]

Thank you so much, Sir It helped me a lot May God bless you for this act of kindness

[@RadfordMathematics]

Thanks Muhammad I truly appreciate you taking the time to write your comment 😊 and really glad to hear it helped! Take good care ✌️

[@jadonw192]

muhammad ali show me ur g

[@alinachen8683]

very well done!

[@RadfordMathematics]

Thanks for your kind comment Alina 😊 I’m really glad it helped ✌️

[@ayandamncedisinyandeni4179]

people havents seen this amazing video ,short ,and easy to understand ,i am soch why you have small suscribers

[@RadfordMathematics]

Thanks for your comment and such kind words Ayanda !! It’s a bit difficult to stand out on KZbin with math videos (there are so many). Most importantly, I’m really glad this video helped 😊 Wishing you all the very best 🌱

[@EmperorDinhira]

❤ best explanation

[@RadfordMathematics]

Thanks 🙏 I’m really glad it helped 😊

[@reecebyron6959]

Very helpful video and clear explanation, thank you so much !

[@halfday6311]

Thanks for the awesome explanation!

[@RadfordMathematics]

Thanks for your kind comment 👍 Really glad this video helped!!! Take good care ✌️

[@abdallakalil290]

👍 Nice great expectation Thanks!!

[@RadfordMathematics]

Thanks for your comment and the kind words 😊 truly glad it helped ✌️

[@tobiasill5790]

great vid man

[@RadfordMathematics]

Thanks for the kind comment Tobias! Really glad it helped 😊

[@weteaman1498]

Thank You

[@thebonezone403]

This video just saved my ass in Vector Calculus

[@RadfordMathematics]

Thanks for the comment!! Really glad it helped 😊

[@nochianand]

Great Video! Thanks for the explanation :)

[@RadfordMathematics]

Thanks for your comment Nochianand, I really appreciate it! Truly glad the video helped 😊 Take good care ✌️

[@FlamzZ]

Thank you so much :)

[@zeden3075]

Thank you so much

[@RadfordMathematics]

Thanks Zeden! I truly appreciate you taking the time to write your comment 😊 I’m really glad it helped!! Take good care ✌️

[@niiazbekmamasaliev9828]

well explained!!!

[@RadfordMathematics]

Hi Niiazbek, thanks for taking the time to write your comment! I really appreciate it 😊 Really glad it helped! You may find the video I made on skew lines useful as well: kzbin.info/www/bejne/amiolKyprpd_pNU Wishing you all the very best ✌️

[@FJ-mn2pi]

Nice.

[@nerdgirl8029]

Amazing video

[@RadfordMathematics]

Thanks for your (very) kind comment @nerdgirl! Truly appreciate it 😊 Really glad this video helped!!

[@rachelfeenstra957]

How do we solve if there is no 0 in the equations? I've noticed that in every youtube video there's a 0, but my teacher gave me a problem with no 0. Thank you.

[@RadfordMathematics]

Hi Rachel, I’m not 100% sure what you’re referring to? Do you mean skew lines? If so, you’ll find my tutorial on that here: kzbin.info/www/bejne/amiolKyprpd_pNU Hope that helps 😊

[@bengarrett6247]

do you mean in the set of values there is a 0 in this particular problem, in that case its the exactly the same process but you have an extra variable you will need to rearrange to solve for z in this case.

[@wetter4293]

The thing that's frustrating is that you did not explain what alpha and beta are... are those supposed to be the distances to get to the second set of coordinates? If so, can I run this calculation with cartesian coordinates at all?

[@swordmatrix6865]

my x and y parametric equations that I created by setting corresponding components from each line equal to each other are the same, so when I subtract them I get 0. Is there a way around this?

[@bruh4196]

Why exactly do we compared the x and y to get alpha and beta and then check it by putting in the third?

[@hosnaroufaidagacem3468]

why do i keep finding different values of alfa and beta each time i use a different pair of equations?

[@elenashevtsova4034]

what's the program that you are using for notes? it's really nice!

[@fecu2394]

A great explanation but that method is impossible to code and rearranging equations is the worst... Surely it can be done with the dot product ignoring all this painful stuff?

[@fecu2394]

Actually, surely we could do this with the determinant..

[@alstjd0808]

thanks daddy!!

[@RadfordMathematics]

Truly glad it helped 😊

[@scriblab]

Excellent! Thanks for this very helpful explanation! Just one question: what happens if in step 3) alpha is not eliminated by subtracting E1-E2? Does one just insert any number (except 0) to have only one unknown? Thanks!

[@Shodan159]

Hi scriblab, If it was not the case that [E1] - [E2] immediately eliminated (alpha), you can multiply either of the equations [E1] or [E2], by any scalar quantity so that (alpha) in both equations is equal and can be subtracted. Additionally, if it is easier, you could manipulate the equation so that for example: in [E1], (alpha) = 2 & in [E2], (alpha) = -2 And then you ADD the equations to eliminate (alpha) ( [E1] + [E2] ), you just have to set it up so one of the two unknown variables can be eliminated. P.S. if you perform any scalar multiplication to the equations, make sure to apply that multiplication to the entire expression. eg. If [E1]: (alpha) + 2(beta) = 10 Then 3 * [E1]: 3(alpha) + 6(beta) = 30

[@Shodan159]

Further more, Say if a scalar multiplication would not result in being able to easily eliminate (alpha), such as: [E1]: 3(alpha) + 3(beta) = 10 [E2]: 7(alpha) - 11(beta) = -5 You could 'Cross-Multiply' the equations by the coefficient of (alpha) for each equation. So, 7 * [E1]: 21(alpha) + 21(beta) = 70 3 * [E2]: 21(alpha) - 33(beta) = -15 Then, you can proceed with ( [E1] - [E2] ).

[@scriblab]

@@Shodan159 Thank you so much for your explanation! :)

[@seangraham577]

@@Shodan159 thanks mr smart man much appreciated

[@emilianoazizaj8654]

What if the third equation of the system isnt proven for the values of alpha and beta?

[@thinsy7825]

What if in 3 you got infinite

[@minhha9570]

can you use the beta eq to achieve the point of intersection?

[@abdelazizmohamed6811]

thank u very much,great explanation hope u become muslim]

[@RadfordMathematics]

I’m truly glad it helped 😊

[@romanschlichter1058]

BEETa

[@manbun3294]

Beetah