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    Decomposition of a vector.

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    Decompose 6i-3j-6k into vectors parallel and perpendicular to following vectors.

    a) i+j+k
    b) 2i-j-2k
    c) 2j-k

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    Solution Preview

    The standard procedure for representing a vector V as a sum of two vectors V_1 and V_2, one parallel to the given one and one perpendicular to the given vector W (thus, decomposing V) is to find the orthogonal projection Proj_W (V) of V onto W (and this will be the vector parallel to W) and then subtract this projection from the original vector V, thus obtaining the perpendicular vector. More ...

    Solution Summary

    The process of decomposing a vector into the sum of components perpendicular and parallel to another vector is examined and illustrated.