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Math Help - Dot products of vectors in three dimensions.

  1. #1
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    Exclamation Dot products of vectors in three dimensions.

    Consider three vectors:

    A = 4 i - 9 j + 6 k
    B = -1 i + 2 j
    C = (6cos60) i + (6sin60) j

    Evaluate the magnitude of the quantity A + (B x C )

    I cannot have a graphing calculator on the test (only a scientific one), so matrices are not possible.

    I tried taking the dot product of B and C and got about 53.65. But then finding the quadrature of the x components, y components, and z components throws me off.

    Help?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by niyati View Post
    Consider three vectors:

    A = 4 i - 9 j + 6 k
    B = -1 i + 2 j
    C = (6cos60) i + (6sin60) j

    Evaluate the magnitude of the quantity A + (B x C )

    I cannot have a graphing calculator on the test (only a scientific one), so matrices are not possible.

    I tried taking the dot product of B and C and got about 53.65. But then finding the quadrature of the x components, y components, and z components throws me off.

    Help?
    there is no dot product here. you have an addition and a cross-product

    here's what you need to know:

    Let \bold {A} be \left< a_1,a_2,a_3 \right> and,
    let \bold {B} be \left< b_1,b_2,b_3 \right>

    then, \bold {A + B} = \left< a_1 + b_1, a_2 + b_2, a_3 + b_3 \right>

    and \bold {A \times B} = \left| \begin {array}{ccc} \bold {i} & \bold {j} & \bold {k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end {array} \right| = (a_2b_3 - a_3b_2) \bold {i} + (a_3b_1 - a_1b_3) \bold {j} + (a_1b_2 - a_2b_1) \bold {k}


    the magnitude of a vector \bold {A} is given by:

    | \bold {A} | = \sqrt {a_1^2 + a_2^2 + a_3^2}
    Last edited by Jhevon; September 23rd 2007 at 06:26 PM. Reason: applied the formatting suggestions of TPH
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  3. #3
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    I was never taught how to do matrices by hand. :S What is the general rule?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by niyati View Post
    I was never taught how to do matrices by hand. :S What is the general rule?
    i gave you the expanded formula as well. it would be a pain to explain here how i did it, you should try looking it up on google and/or wikipedia
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  5. #5
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    Already done.

    Thank you for your help!
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  6. #6
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    Instead of using  < \ \ \ > use \left< \ \ \ \right> to make it look nicer.
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