Results 1 to 4 of 4

Math Help - Please tell me why?

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    123

    Question 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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member TriKri's Avatar
    Joined
    Nov 2006
    Posts
    358
    Thanks
    1
    Quote Originally Posted by Jenny20 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    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

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2006
    Posts
    123
    Thank you very much Soroban! Your explaination is very clear to me.

    A little. I am learning cross product now.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum