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Math Help - Dot and Scalar Product

  1. #1
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    Dot and Scalar Product

    I have been lost in this forever due to missing the lecture, but does anybody know how to do this? Thank you for the help if you can.
    a=3.0i+3.0j-2.0k
    b=-1.0i-4.0j+2.0k
    c=2.0i+2.0j+1.0k
    The question is: a(dot)(axb)=?

    Any help would be appreciated.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Elite_Guard89 View Post
    I have been lost in this forever due to missing the lecture, but does anybody know how to do this? Thank you for the help if you can.
    a=3.0i+3.0j-2.0k
    b=-1.0i-4.0j+2.0k
    c=2.0i+2.0j+1.0k
    The question is: a(dot)(axb)=?

    Any help would be appreciated.
    What you are asked to evaluate here is what is know as the scalar triple product.

    \bold a\cdot\left(\bold b\times\bold c\right)=\left|\begin{array}{ccc}a_x&a_y&a_z\\b_x&  b_y&b_z\\c_x&c_y&c_z\end{array}\right|

    Try to evaluate \left|\begin{array}{ccc}3&3&-2\\-1&-4&2\\2&2&1\end{array}\right|

    This will give you the desired answer.

    I hope this helps!

    --Chris
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  3. #3
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    Okay, then how would you do a(dot)(b+c)?
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  4. #4
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    Add the vectors b and c to get b + c. Then take the dot product of a and what you found?
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  5. #5
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    I understand the b+c part, but I'm not sure on how you find the dot product of a and what (b+c) creates.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Elite_Guard89 View Post
    I understand the b+c part, but I'm not sure on how you find the dot product of a and what (b+c) creates.
    When you take the dot product of a and this new vector (b+c), we get a scalar value. You multiply the like components together, and then add them all together. Note that \bold i\cdot\bold i=\bold j\cdot\bold j=\bold k\cdot\bold k=1

    I hope this helps!

    --Chris
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  7. #7
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    Why not?

    \bold{b} + \bold{c} = (-1.0 + 2.0) \bold{i} + (- 4.0  + 2.0) \bold{j} + (2.0 + 1.0) \bold{k} = 1.0 \bold{i} - 2.0 \bold{j} + 3.0\bold{k}

    So: \bold{a} \cdot (\bold{b} + \bold{c}) = (3.0 \bold{i} + 3.0 \bold{j} - 2.0 \bold{k}) \cdot (1.0 \bold{i} - 2.0 \bold{j} + 3.0\bold{k})

    Surely you can take the dot product of two vectors?
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  8. #8
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    I would if I knew what a dot product was lol.
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  9. #9
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Elite_Guard89 View Post
    I would if I knew what a dot product was lol.
    The definition of the dot product:

    If \bold a=\left<a_x,a_y,a_z\right> and \bold b=\left<b_x,b_y,b_z\right>, the the dot product of a and b is:

    \bold a\cdot\bold b=a_xb_x+a_yb_y+a_zb_z

    I hope this helps!

    --Chris

    w00t!!! My 8th post!!
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