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Math Help - cross product

  1. #1
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    Question cross product

    Can you explain to me why

    (sint i + cost j) x (cost i - sint j) = -sin^2t k - cos^2t k ?

    where i , j, k are unit vectors.


    Thank you very much.
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  2. #2
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    Quote Originally Posted by Jenny20 View Post
    Can you explain to me why

    (sint i + cost j) x (cost i - sint j) = -sin^2t k - cos^2t k ?

    where i , j, k are unit vectors.
    Thank you very much.
    Hello, Jenny,

    I only know the cross product with vectors. To use vectors I re-write your problem:

    v_1 = (sin(t), cos(t), 0)

    v_2 = (cos(t), -sin(t), 0)

    Now calculate the cross-product:

    \begin{array}{|ccc|}i&j&k \\ \sin(t) & \cos(t) & 0 \\ \cos(t) & -\sin(t) &0 \end{array} =(0, 0, \sin(t) \cdot (-\sin(t))-\cos(t) \cdot \cos(t))

    Maybe this helps a little bit further.

    EB
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  3. #3
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    Hello, Jenny!

    Can you explain to me why

    \left[(\sin t)\vec{i} + (\cos t)\vec{j}\right] \times  \left[(\cos t)\vec{i} - (\sin t)\vec{j}\right] \:=\: \left(\text{-}\sin^2t - \cos^2t\right)\vec{k} ?
    Do you know how to find a cross product?


    We have two vectors: . \vec{u}\:=\:\langle \sin t,\,\cos t,\,0\rangle and \vec{v}\:=\:\langle\cos t,\,\text{-}\sin t,\,0\rangle

    . . Then: . \vec{u} \times \vec{v}\;=\;\begin{vmatrix}\vec{i} & \vec{j} & \vec{k} \\ \sin t & \cos t & 0 \\ \cos t & \text{-}\sin t & 0 \end{vmatrix}

    Now crank it out: . \vec{i}(\cos t\cdot0 + \sin t\cdot0) - \vec{j}(\sin t\cdot0 - \cos t\cdot0) + \vec{k}(-\sin^2t - \cos^2t)

    Got it?

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