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Math Help - Component of a vector in direction of another

  1. #1
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    Component of a vector in direction of another

    Practice problem asks for the component of vector A=(2,1,-4) in the direction of B=(1,2,3).

    I've found the direction vector of B (by dividing B by its length of √14). Let's call this direction vector d.

    Now, is the dot product (x.d) the answer?
    I found -8/√14
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  2. #2
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    Quote Originally Posted by keysar7 View Post
    Practice problem asks for the component of vector A=(2,1,-4) in the direction of B=(1,2,3).

    I've found the direction vector of B (by dividing B by its length of √14). Let's call this direction vector d.

    Now, is the dot product (x.d) the answer?
    I found -8/√14
    You have found the dot product x.d correctly. But the answer to the question should be a vector, not a scalar. The component of A in the direction of B is the vector (x.d)d (its magnitude is x.d and its direction is given by the direction of d). So the answer should be \frac{-8}{14}(1,2,3).
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  3. #3
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    Opalg, many books use the opposite convention- that the "component" of a vector in a given direction is a scalar. For example, the "component" of <a, b, c> in the <1, 0, 0> direction is "a", not <a, 0, 0>. keysar7, better check your textbook or with your teacher to be sure which convention is being used.
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