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    western50's Avatar
    western50 Posts: 105, Reputation: 1
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    #1

    Jun 20, 2011, 08:16 AM
    vectors
    So I have these two vectors
    X=3 {Cos[\[Pi]/3],Sin[\[Pi]/3]};
    Y={Cos[\[Pi]/6],Sin[\[Pi]/6]};
    and I want to obtain two other vectors U and V such that obey the following conditions:

    U parallel to Y
    V perpendicular to Y
    X = U+V

    I have tried many ways but still can't get the answer for U and V, please help me on this!
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Jun 20, 2011, 09:49 AM

    Let A equal the magnitude of . Since you know is parallel to , it's operating in the direction . Break it into its x and y components:



    The vector that is perpendicular to Y has magnitiude B, and is in the direction of plus :



    Now add the x components of the and vectors together, and set this equal to the x component of your vector, and do the same for the y components. This will give you two equations in 2 unknowns; solve for A and B.

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