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Math Help - component of one vector in the direction of another

  1. #1
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    component of one vector in the direction of another

    Find the component of c = <2, 1> in the direction v = <4, 1>. Hence
    write c in the form c = λv + w, where v w = 0.
    Check also that w itself is the component of c in the direction w.

    thanks for any help
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  2. #2
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    Quote Originally Posted by hmmmm View Post
    Find the component of c = <2, 1> in the direction v = <4, 1>. Hence
    write c in the form c = λv + w, where v w = 0.
    Check also that w itself is the component of c in the direction w.

    thanks for any help
    1. Calculate the direction of \vec w = (w_1, w_2):

    (2,1) \cdot \vec w = 0~\implies~ \vec w = (w_1,-4w_1)

    2. Now use the given equation:

    \lambda \cdot (4,1) + (w_1, -4w_1)=(2,1)

    Solve for \lambda and w_1

    3. Make a sketch to control your calculations.
    Attached Thumbnails Attached Thumbnails component of one vector in the direction of another-vektor_komponentenzerlegung.png  
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