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Vectors a and b have magnitudes 2 and 3, respectively. If one of them is 50degrees, find the vector 5a-2b and state its magnitude.

  • Vectors - ,

    Use the law of cosines: You know two sides, and the included angle.

    Draw the figure before you compute.

  • Vectors - ,

    I tried that but it doesn't work.

    I did (5)(2^2)+(2)(3^2)-(2)(2)(3)cos50.

  • Vectors - ,

    vector 5a has magnitude 10 and call it at 50 degrees
    vector 2 b has magnitude 6 and call it at 0 degrees
    so our triangle is
    10 and 6 with fifty degrees between them
    so the magnitude we are looking for is from
    c^2 = 10^2 + 6^2 - 10*6*cos 50
    that is why it did not work.

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