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Math Help - Vector Projections

  1. #1
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    Vector Projections

    I'm given two vectors: F=9i+12j, V=3i+4j. I am asked to give the component of F parallel to V, the component of F perpendicular to V and the work done by force F through displacement V.

    Any help?
    Peter
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  2. #2
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    Well you can express F as:

    \vec{F} = 3(3i + 4j)

    Meaning that F is parallel to V.

    Find the magnitude of F (using the Pythagoras' Theorem) this will be the parallel component.

    The perpendicular component will be 0 since the two vectors are parallel.

    Work Done = Force x Displacement.

    Find the magnitude of the displacemnt V and you already have the force F, which is the parallel component of F to V.
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  3. #3
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    Quote Originally Posted by flybynight View Post
    I'm given two vectors: F=9i+12j, V=3i+4j. I am asked to give the component of F parallel to V, the component of F perpendicular to V and the work done by force F through displacement V.
    F_\parallel   = \frac{{F \cdot V}}<br />
{{V \cdot V}}V\;\& \,F_ \bot   = F - F_\parallel  <br />
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