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Math Help - Vector Math Help

  1. #1
    Junior Member
    Joined
    Aug 2009
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    Question Vector Math Help

    The question is,

    Let K be a scalar and let U = (Ux,Uy,Uz). Prove that ||kU|| = |k| ||U||

    I'm not entirely sure what the question is asking here, I'm getting confused with the meaning of the bars ||kU|| and |k| and ||U||.

    I'd think ||kU|| would be U = (k * Ux, k* Uy, k * Uz).

    Would it be better to prove this scenario by assigning the variables values, like let k = 6, U = (-5, 4, 8). So ||6U|| = (6 * -5, 6 * 4, 6 * 8).

    I think my problem might be stemming from not understanding the question or I might just be losing the plot.
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  2. #2
    Senior Member
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    Hi RedKMan

    Usually in proofing, you're not allowed to substitute numerical value. Maybe this will do :

    If U=\left(\begin{array}{cc}U_x\\U_y\\U_z\end{array}\  right) , then :

    |U| = \sqrt{(U_x)^2+(U_y)^2+(U_z)^2}

    For :  kU = \left(\begin{array}{cc}kU_x\\kU_y\\kU_z\end{array}  \right)

    |kU| =  \sqrt{(kU_x)^2+(kU_y)^2+(kU_z)^2}

    =\sqrt{k^2((U_x)^2+(U_y)^2+(U_z)^2)}

    =|k| \sqrt{(U_x)^2+(U_y)^2+(U_z)^2}

    =|k||U|
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  3. #3
    Junior Member
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    Hi Songoku,

    Thanks for reply, I am still struggling to understand this.

    I'm not sure how your answer proves that ||kU|| = |k| ||U||.
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  4. #4
    MHF Contributor
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    Quote Originally Posted by RedKMan View Post
    I'm not sure how your answer proves that ||kU|| = |k| ||U||.
    It does

    songoku has proven ||kU|| = |k|\:||U|| or in other words : the modulus of the product of a scalar k and a vector U is equal to the product of the absolute value of k and the modulus of U
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