A community for students.
Here's the question you clicked on:
 0 viewing
Noliec
 2 years ago
If u+v+w=0, show that u x v = v x w = w x u.
Noliec
 2 years ago
If u+v+w=0, show that u x v = v x w = w x u.

This Question is Closed

Noliec
 2 years ago
Best ResponseYou've already chosen the best response.0Initially 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.

Noliec
 2 years ago
Best ResponseYou've already chosen the best response.0Currently at vxu+vxw+wxu

Noliec
 2 years ago
Best ResponseYou've already chosen the best response.0Quite certain you're supposed to use the fact that some of the vector products are orthogonal to each other and therefore 0

Noliec
 2 years ago
Best ResponseYou've already chosen the best response.0Just 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?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1So 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(u2v3u3v2)j(u1v3v1u3)+k(u1v2u2v2) 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.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1You would write your ui's as wi's by using ui+vi+wi=0 as ui=(wi+vi)

Noliec
 2 years ago
Best ResponseYou've already chosen the best response.0Indeed, 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.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Hey! We use some cool properties!? :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Like 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.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Because 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
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.