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17 March, 18:41

Find the angle 0 between the vectors. u = (1, 1, 1, 0), v = (4, 4, 4, 4).

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  1. 17 March, 21:28
    0
    30 degrees

    Step-by-step explanation:

    u dot v=1*4+1*4+1*4+0*4=4+4+4+0=12

    |u|=sqrt (1^2+1^2+1^2+0^2) = sqrt (3)

    |v|=sqrt (4^2+4^2+4^2+4^2) = sqrt (4*4^2) = 2*4=8

    cos (theta) = u dot v / (|u||v|)

    cos (theta) = 12 / (sqrt (3) * 8)

    cos (theta) = 3 / (sqrt (3) * 2)

    cos (theta) = sqrt (3) / 2

    theta=30 degrees
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