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Math Help - Vector proofs urgent help needed

  1. #1
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    Exclamation Vector proofs urgent help needed

    For each of the following statements, determine whether it is true or false. If the statement is true then prove it; if it is false then give an example where the statement fails to hold.
    (i) If
    u, v,w is a right-handed triple of vectors, with u orthogonal to v, then v must be orthogonal to w.

    (ii) (
    u v) w = u (v w) for all vectors u, v,w.

    (iii) If
    u v = v u then we must have u v = 0.


    (iv) If
    u is a vector such that u v = 0 for every vector v, then we must have u = 0.


    can some one help me asap i dnt knw wer 2 start .
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  2. #2
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    Quote Originally Posted by omarj View Post
    For each of the following statements, determine whether it is true or false. If the statement is true then prove it; if it is false then give an example where the statement fails to hold.
    (i) If
    u, v,w is a right-handed triple of vectors, with u orthogonal to v, then v must be orthogonal to w.

    What is the DEFINITION of "right-handed triple" of vectors?

    (ii) (
    u v) w = u (v w) for all vectors u, v,w.

    Surely at the time you learned about the cross product you learned the fact, if not the proof, that u x v is associative. What does that mean?

    [quote[(iii) If
    u v = v u then we must have u v = 0.
    [/quote]
    The cross product, u x v, is anti-symmetric. What does that mean?

    (iv) If
    u is a vector such that u v = 0 for every vector v, then we must have u = 0.


    can some one help me asap i dnt knw wer 2 start .
    One definition of cross prioduct u x v is that it is the vector that is perpendicular to both u and v (in the "right-hand" sense) with length equal to |u||v|cos(\theta). Since this says u x v= 0 for every vector v, try taking v to be a vector that is perpendicular to u and has length 1. What is the length of |u x v|?
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  3. #3
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    Smile

    thanks that helped alot
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