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Math Help - vector componets

  1. #1
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    vector componets

    Let u = 3i - 4j + 12k, and v = 2i + 2j - k

    find 5u - 2v

    find the length of u

    find the length of v

    find u * v

    and find the angle between u and v. give your answer to the nearest 0.01

    radians.

    any help with these please.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    Let u = 3i - 4j + 12k, and v = 2i + 2j - k

    find 5u - 2v

    find the length of u

    find the length of v

    find u * v

    and find the angle between u and v. give your answer to the nearest 0.01

    radians.

    any help with these please.
    u = 3i - 4j + 12k, and v = 2i + 2j - k

    find 5u - 2v

    <15, -20, 60> - <4, 4, -2> = <11, -24, 62>

    find the length of u

    sqrt(9 + 16 + 144) = sqrt(169) = 13

    find the length of v

    sqrt(4 + 4 + 1) = sqrt(9) = 3

    find u * v (I'm assuming it is u dot v).

    u.v = 6 + (-8) + (-12) = -14

    find the angle between u and v. give your answer to the nearest 0.01

    radians.

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

    -14/(13*3) = cos(theta)

    -14/39 = cos(theta)

    arccos(-14/39) = theta

    And thus, the angle is: 1.94 radians.
    Last edited by AfterShock; March 6th 2007 at 08:39 PM. Reason: Edit: finding angle w/ dot prod is cos, not sin.
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