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Math Help - Dot product and Angle

  1. #1
    Member nautica17's Avatar
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    Dot product and Angle

    This is a question from calculus 3 class.

    "Find the dot product of the vectors and the cosine of the angle between them."

    u = i - 3j + 7k
    v = 8i - 2j - 2k

    Okay, I get what to do, and I get answers but apparently they're wrong according to the back of the book. What am I doing wrong?

    My work:
    u dot v = (1*8) + (-3*-2) + (7*-2) = 28 = dot product

    ||u|| = sqrt(1^2 + (-3)^2 + 7^2) = sqrt(59)
    ||v|| = sqrt(8^2 + (-2)^2 + (-2)^2) = 6*sqrt(2)

    (28) / ( sqrt(59) * (6*sqrt(2)) ) = .429601
    cos^-1 (.429601) = 1.12675 radians = angle

    Edit: The book says the dot product is 0 and the angle is also 0.
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  2. #2
    A Plied Mathematician
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    (1*8) + (-3*-2) + (7*-2) = 8 + 6 - 14 = 0.

    If the book says that the angle is also 0, they're wrong. But if, as I suspect, they mean that the cosine of the angle is zero, they'd be correct.
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  3. #3
    Member nautica17's Avatar
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    Ahh I see.. I added 14 for some reason.. even though I went through this 3 times already. :| I think I got the angle working too now.

    Thanks!
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  4. #4
    A Plied Mathematician
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    No problem. Have a good one!
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