# Vector exemple

• Dec 4th 2012, 02:08 AM
Petrus
Vector exemple
Attachment 26051Hello i kinda got confused on a exemple, it says show that the dioganal (i think it spell so in english) in a romb is ortogonal.
so i dont get the first part where u say AB is positive then on second parentes AB is negataiv??? Well i think it should be AC•AB=(AB+BC)•(AB-AD) can some1 explain why is it not like i think?
• Dec 4th 2012, 03:13 AM
BobP
Re: Vector exemple
$\displaystyle \underline{BD}=\underline{BA}+\underline{AD}= \underline{AD}+\underline{BA}=\underline{AD}-\underline{AB}$
• Dec 4th 2012, 03:19 AM
Petrus
Re: Vector exemple
Ty now i got it but on the third step where does the BC•BC COME FROM?
• Dec 4th 2012, 04:17 AM
BobP
Re: Vector exemple
$\displaystyle \underline{AD}=\underline{BC}.$
Two vectors are equal if they have the same magnitude and the same direction.
• Dec 4th 2012, 05:57 AM
Petrus
Re: Vector exemple
ok now i got it ty alot :)
• Dec 4th 2012, 06:08 AM
Plato
Re: Vector exemple
Quote:

Originally Posted by Petrus
diagonal (i think it spell so in english) in a rhombus is orthogonal.

Part of the difficulty is notation. Let $\displaystyle \vec{u}=\overrightarrow {AD} ~\&~\vec{v}=\overrightarrow {AB}$.

Now the two diagonals are $\displaystyle \vec{u}+\vec{v}~\&~\vec{u}-\vec{v}$

Look at $\displaystyle (\vec{u}+\vec{v})\cdot(\vec{u}-\vec{v})=\|\vec{u}\|^2-\|\vec{v}\|^2=0$
because in a rhombus the sides have equal lengths .