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March 25, 2017

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You are given vectors A = 5.0i - 6.5j & B = -3.5i + 7.0j. A third vector C lies on the xy-plane. Vector C is perpendicular to vector A, & the scalar product of C with B is 15.0. From this information, find the components of vector C.

  • Physics - ,

    A=[5,-6.5]
    B=[-3.5,7]

    If A is perpendicular to C, then A.C=0, or
    C=[6.5k, 5k]
    (verify that A.C=0)

    If in addition, C.B=15, we have
    C.B=[6.5k,5k].[-3.5,7]
    =35k-22.75k
    =12.25k

    But C.B=15, therefore 12.25k=15, =>
    k=15/12.25=60/49

    Therefore
    C=[6.5k,5k]
    =[390/49, 300/49]

    Check my arithmetic and that the given conditions are satisfied.

  • Physics - ,

    thanks

  • Physics :) - ,

    you're welcome!

  • Physics - ,

    I don't understand the flow in the math here. Please help me understand this solution by "dumbing it down" a bit.

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