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Math Help - vector calc

  1. #1
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    vector calc

    prove that b x a = -a x b

    i know how to do it if i make like an example with numbers but how can i show this otherwise? anyone want to start off the proof for me, i'm just kind of stuck
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  2. #2
    MHF Contributor Calculus26's Avatar
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    you've got the right idea

    just start with a = a1i +a2j +a3k and b = b1 i + b2j +b3k

    and then just brute force and ignorance

    also it is obvious from the right hand rule but I don't think you want
    to hand in pictures of your hands
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  3. #3
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    so i started with
    b x a= (a3*b2-a2*b3, a1*b3-a3*b1, a2*b1-a1*b2)
    a x b= (a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)

    how should i show that b x a= -a x b
    should i just put numbers into what i have above?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Nice work

    to finish you could say by inspection a x b = -b x a

    or - a x b = -(a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)

    = (a3*b2-a2*b3, a1*b3-a3*b1, a2*b1-a1*b2)

    = b x a
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  5. #5
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    thank you very much
    sorry for bugging you i just have one more question i promise
    i am finding the area of the triangle with vertices (0,6,0) (-5,7,1) and (2,1,2)

    i got a= (5,-1,-1) and b= (7,-6,1)
    and i think the formula is A= 1/2 ll a x b ll
    so then i did the square root of the determinates squared and got the square root of (-5)^2 + (-2)^2 + (37)^2 which is definitely not right

    the answer is 19/sqrt of 2...
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  6. #6
    MHF Contributor Calculus26's Avatar
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    A couple of small mistakes computing a x b

    a x b = -7 i -12 j -23 k

    See attachment--signs are always a pain in the ass when doing determinants
    Attached Thumbnails Attached Thumbnails vector calc-areavectholly.jpg  
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  7. #7
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    oh man i made some dumb mistakes haha i think i just couldn't see them because i was getting so frustrated and tired of doing my homework. thanks so much!
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  8. #8
    MHF Contributor Calculus26's Avatar
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    The imprtant thing is you have the right skills

    1. you knew you needed 1/2(axb)

    2.you knew how obtain the vectors a and b

    these are very encouraging signs
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