# Please tell me why?

• Dec 5th 2006, 12:27 AM
Jenny20
Please tell me why?
If U= <-3,-2,2> and V=<-2,2,3> , then

Why U X V = <-10,5,-10> ? Would you please explain to me by showing its working steps? Thank you very much.

Note : U and V are vectors.
• Dec 5th 2006, 04:35 AM
TriKri
Quote:

Originally Posted by Jenny20
If U= <-3,-2,2> and V=<-2,2,3> , then

Why U X V = <-10,5,-10> ? Would you please explain to me by showing its working steps? Thank you very much.

Note : U and V are vectors.

If $\displaystyle V_1 = (a_1,\ b_1,\ c_1)$ and $\displaystyle V_2 = (a_2,\ b_2,\ c_2)$, then $\displaystyle V_1\times V_2 = (b_1\cdot c_2-b_2\cdot c_1,\ c_1\cdot a_2-c_2\cdot a_1,\ a_1\cdot b_2-a_2\cdot b_1)$

A vector product is often called a cross product and you can read more about it here.
• Dec 5th 2006, 10:02 AM
Soroban
Hello, Jenny!

Do you know what a cross product is?

Quote:

If $\displaystyle \vec{u}\:=\:\langle-3,-2,2\rangle$ and $\displaystyle \vec{v}\:=\:\langle-2,2,3\rangle$, find $\displaystyle \vec{u} \times \vec{v}$

You are expected to familiar with determinants.

$\displaystyle \vec{u} \times \vec{v}\;=\;\begin{vmatrix}i & j & k \\ \text{-}3 & \text{-}2 & 2 \\ \text{-}2 & 2 & 3\end{vmatrix}\;=\;i\begin{vmatrix}\text{-}2 & 2 \\ 2 & 3\end{vmatrix} - j\begin{vmatrix}\text{-}3 & 2 \\ \text{-}2 & 3\end{vmatrix} + k\begin{vmatrix}\text{-}3 & \text{-}2 \\ \text{-}2 & 2\end{vmatrix}$

. . . . $\displaystyle = \;i(\text{-}6-4) - j(\text{-}9+4) + k(\text{-}6-4) \;=\;-10i + 5j - 10k$

Therefore: .$\displaystyle \vec{u} \times \vec{v} \;=\;\langle\text{-}10,\,5,\,\text{-}10\rangle$

• Dec 5th 2006, 07:06 PM
Jenny20
Thank you very much Soroban! Your explaination is very clear to me.

A little. I am learning cross product now.