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Math Help - Some vector algebra problems.

  1. #1
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    Some vector algebra problems.

    1.Find \vec{a} x \vec{b}(Vectorial product) if \vec{a}=3\vec{m}+2\vec{n}, \vec{b}=\vec{m}+5\vec{n} and |\vec{m}|=|\vec{n}|=1. (Angle between m and n is 90 degrees.)

    2.We have vectors \vec{a}=(0,2\lambda,\lambda), \vec{b}=(2,2,1) and \vec{c}=(-1,-2,-1)

    a) Find \vec{d} from this conditions: \vec{a}x\vec{b} = \vec{c}x\vec{d} and \vec{a}x\vec{c} = \vec{b}x\vec{d} (Vectorial product).
    b) Prove that vectors \vec{a} - \vec{d} and vectors \vec{b} - \vec{c} are colinear.
    c) Find \lambda from condition (\vec{a}-\vec{b})*\vec{c}=\vec{a}*\vec{c}+\lambda

    3. Write equation of normal from point M(2,3,1) into line: l: \frac{x+1}{2}=\frac{y-0}{-1}=\frac{z-2}{3}.

    Thank you.
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  2. #2
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    The first one should go like shown below.
    Attached Thumbnails Attached Thumbnails Some vector algebra problems.-f.gif  
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  3. #3
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    logic, it's vectorial (cross) product. Any idea for these problems?

    Anyway thank you.
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  4. #4
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    Quote Originally Posted by GreenMile View Post
    1.Find \vec{a} x \vec{b}(Vectorial product) if \vec{a}=3\vec{m}+2\vec{n}, \vec{b}=\vec{m}+5\vec{n} and |\vec{m}|=|\vec{n}|=1. (Angle between m and n is 90 degrees.)

    [snip]
    Note that m x m = n x n = 0. Nothing much can be said about m x n except that it will be another vector perpendicular to m and n and that its magnitude will be equal to 1.
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