Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Noliec

  • one year ago

If u+v+w=0, show that u x v = v x w = w x u.

  • This Question is Closed
  1. Noliec
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Initially I set u=(-1)(v+w), v=(-1)(u+w), w=(-1)(u+v) and then try to just insert those vectors into the thing I'm supposed to show; I don't know how to go from where I am though.

  2. Noliec
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Currently at vxu+vxw+wxu

  3. Noliec
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Quite certain you're supposed to use the fact that some of the vector products are orthogonal to each other and therefore 0

  4. Noliec
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Just arrived at wxu; still haven't shown for vxw though, it seems very chaotic just inserting relations over and over, is there a better way?

  5. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So say we have u=(u1,u2,u3) v=(v1,v2,v3) w=(w1,w2,w3) ,then u1+v1+w1=0 u2+v2+w2=0 u3+v3+w3=0. uxv= |dw:1380907086373:dw| =i(u2v3-u3v2)-j(u1v3-v1u3)+k(u1v2-u2v2) SO I guess you could use this to show wxu by writing what I just wrote but your ui's as wi's and your vi's as ui's. (Then do the same for vxw) But this seams pretty long to me. I will have to see if I can find a shorter way.

  6. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You would write your ui's as wi's by using ui+vi+wi=0 as ui=-(wi+vi)

  7. Noliec
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Indeed, that's what I went for, managed to show that the left term was the right term; never got to the middle one though. It seems like a mess using the laws though.

  8. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hey! We use some cool properties!? :)

  9. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Like can we use ax(b+c)=(axb)+(axc) This would cut out a lot of time. This would make the proof like 100 times easier.

  10. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Because since w=-(u+v), then w=-u+(-v) So vxw=vx(-u+(-v)) =vx(-u) + vx(-v) Then we can also use -bxa=axb and use axa=0

  11. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.