# Math Help - Please tell me why?

1. ## 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.

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

A vector product is often called a cross product and you can read more about it here.

3. Hello, Jenny!

Do you know what a cross product is?

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

You are expected to familiar with determinants.

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

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

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

4. Thank you very much Soroban! Your explaination is very clear to me.

A little. I am learning cross product now.