Calculus

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For which value(s) of k will the dot product of the vectors (k,2k-1, 3) and (k,5,-4) be 7?

I did this so far,

2k-1=5
6/2

k=3

  • Calculus -

    what's the problem?

    (k,2k-1,3)•(k,5,-4) = k*k + (2k-1)(5) + 3(-4)

    so, we need

    k^2 + 10k - 5 - 12 = 7
    k^2 + 10k - 24 = 0
    (k-2)(k+12) = 0
    so, k=2 or -12

    k=2: (2,3,3)•(2,5,-4) = 4+15-12 = 7
    k=-12: (-12,-25,3)•(-12,5,-4) = 144-125-12 = 7

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