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Thread: Showing that two vectors are perpendicular

  1. #1
    New Member
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    Feb 2012
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    Showing that two vectors are perpendicular

    Regarding the problem:

    Show that for any vectors [TEX]\vec{a}[/TEX], [TEX]\vec{b}\in{R^3}[/TEX],
    [TEX]\vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}[/TEX] and [TEX]\vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}[/TEX]
    are perpendicular

    I'm not exactly sure where to begin with this problem. I think maybe taking the dot product of u and v but I'm not sure.

  2. #2
    Elite Member
    Join Date
    Jan 2005
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    Quote Originally Posted by gmer View Post
    Show that for any vectors [TEX]\vec{a}[/TEX], [TEX]\vec{b}\in{R^3}[/TEX],
    [TEX]\vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}[/TEX] and [TEX]\vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}[/TEX]
    are perpendicular

    I'm not exactly sure where to begin with this problem. I think maybe taking the dot product of u and v but I'm not sure.
    What does [TEX]\vec{u}\cdot\vec{v}=~?[/TEX]
    Hint: Recall that [TEX]\vec{a}\cdot\vec{a}=\|a\|^2.[/TEX]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

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