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Math Help - 3D Vector Word Problem Help

  1. #1
    Junior Member Morphayne's Avatar
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    Exclamation 3D Vector Word Problem Help

    Problem:

    Determine the value of m so that the vectors u=[4, -2, 6] and v=[6, m, 9] are:

    a) Parallel
    b) Perpendicular

    Answers: a) -3
    b) 39

    Comments:

    Please help me!
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  2. #2
    Moo
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    Hi !

    Quote Originally Posted by Morphayne View Post
    Problem:

    Determine the value of m so that the vectors u=[4, -2, 6] and v=[6, m, 9] are:

    a) Parallel
    b) Perpendicular

    Answers: a) -3
    b) 39

    Comments:

    Please help me!
    If two vectors are parallel, there exists a real number x, different to 0, such that :
    \vec{u}=x \vec{v}

    So seeing that 4={\color{red}\frac 23} \cdot 6 and 6={\color{red}\frac 23} \cdot 9, can you set up a relation between -2 and m ?

    ------------------------------
    Now, if two vectors are perpendicular, this means that the dot product is 0.
    For two vectors : u=\begin{pmatrix} u_1 \\ u_2 \\ u_3 \end{pmatrix} and v=\begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}, their dot product is :

    u_1v_1+u_2v_2+u_3v_3

    So here, what is the dot product of u and v ? Deduce the value of m ?
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  3. #3
    Eater of Worlds
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    The vectors are perpendicular when the dot product is 0.

    4(6)+(-2)m+6(9)=0

    Solve for m
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  4. #4
    Junior Member Morphayne's Avatar
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    Quote Originally Posted by Moo View Post
    If two vectors are parallel, there exists a real number x, different to 0, such that :
    \vec{u}=x \vec{v}

    So seeing that 4={\color{red}\frac 23} \cdot 6 and 6={\color{red}\frac 23} \cdot 9, can you set up a relation between -2 and m ?

    ------------------------------
    Now, if two vectors are perpendicular, this means that the dot product is 0.
    For two vectors : u=\begin{pmatrix} u_1 \\ u_2 \\ u_3 \end{pmatrix} and v=\begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}, their dot product is :

    u_1v_1+u_2v_2+u_3v_3

    So here, what is the dot product of u and v ? Deduce the value of m ?
    I don't quite understand the explanation of the parallel part.
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  5. #5
    Moo
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    Quote Originally Posted by Morphayne View Post
    I don't quite understand the explanation of the parallel part.
    There is a constant ratio between each coordinates of the two vectors, if they are parallel

    Between 4 and 6, between -2 and m and between 6 and 9.

    That is to say : \frac 46=\frac{-2}m=\frac 69=x (the one I defined above )

    I hope this helps :x
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  6. #6
    Junior Member Morphayne's Avatar
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    Could I get away with doing this:

    -2/m=2/3

    m=3(-2)/2

    m=-3/1

    m=-3

    And BTW, is there a tutorial on how to use that fancy math text?
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  7. #7
    Moo
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    Quote Originally Posted by Morphayne View Post
    Could I get away with doing this:

    -2/m=2/3

    m=3(-2)/2

    m=-3/1

    m=-3

    And BTW, is there a tutorial on how to use that fancy math text?
    This is exactly what you have to do


    For this fancy math text, see this section : http://www.mathhelpforum.com/math-help/latex-help/, especially this thread : http://www.mathhelpforum.com/math-he...-tutorial.html

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  8. #8
    Junior Member Morphayne's Avatar
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    Moo, do you mind helping with one more? I posted it a short while back and I didn't understand the reply because the person was using techniques that I haven't even studied yet.

    http://www.mathhelpforum.com/math-he...blem-help.html
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