My Math Forum

My Math Forum (http://mymathforum.com/math-forums.php)
-   Abstract Algebra (http://mymathforum.com/abstract-algebra/)
-   -   vector proving (http://mymathforum.com/abstract-algebra/333914-vector-proving.html)

panky July 14th, 2016 12:10 AM

vector proving
 
Let $\displaystyle \vec{a},\vec{b},\vec{c},\vec{d}$ are four distinct vectors satisfying

$\displaystyle \vec{a}\times\vec{b}=\vec{c}\times\vec{d}$ and $\displaystyle \vec{a}\times\vec{c}=\vec{b}\times\vec{d}$. Then

Show that $\displaystyle \vec{a}.\vec{b}+\vec{c}.\vec{d}\neq\vec{a}.\vec{c} +\vec{b}.\vec{d}$

zylo September 8th, 2016 07:58 PM

axb=cxd
axc=bxd
subtract
(a-d)x(b-c)=0

assume
a.b+c.d=a.c+b.d
then
(a-d).(b-c)=0
Contradiction. Two vectors can't be parallel and perpendicular simultaneously.


All times are GMT -8. The time now is 07:36 AM.

Copyright © 2018 My Math Forum. All rights reserved.