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Math Help - distance

  1. #1
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    distance

    ima calculate distance between line L1=(x,y,z)=(3+t,1+t,2-2t) t is rreal number and line L2 its a linear equation x+2=0 is a top and bottom y=3
    my progress:
    L1=(3,1,2)+t(1,1,-2)
    L2 z=s x=-s y=3 (x,y,z)=(0,3,0)+s(-1,0,1)
    Last edited by Petrus; December 15th 2012 at 07:44 AM.
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  2. #2
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    Re: distance

    Quote Originally Posted by Petrus View Post
    line L2 its a linear equation x+2=0 is a top and bottom y=3

    Sorry, but your description of L_2 makes no sense.

    Please try again.
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  3. #3
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    Re: distance

    Here is a pic L2distance-image.jpg
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  4. #4
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    Re: distance

    Quote Originally Posted by Petrus View Post
    ima calculate distance between line L1=(x,y,z)=(3+t,1+t,2-2t) t is rreal number and line L2 its a linear equation x+2=0 is a top and bottom y=3
    my progress:
    L1=(3,1,2)+t(1,1,-2)
    L2 z=s x=-s y=3 (x,y,z)=(0,3,0)+s(-1,0,1)
    Now that is a bit clearer. You must prove that these are two skew lines.

    If \ell_1:P+tD~\&~\ell_2:Q+sE are a pair of skew lines then:

    D(\ell_1,\ell_2)=\frac{|(Q-P)\cdot(D\times E)|}{\|D\times E\|}
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  5. #5
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    Re: distance

    ik that Q-P=-3,2,-2 but i dont know how to calculate D x E
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  6. #6
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    Re: distance

    Quote Originally Posted by Petrus View Post
    ik that Q-P=-3,2,-2 but i dont know how to calculate D x E

    D\times E=\left| {\begin{array}{rrr}   i & j & k  \\   1 & 1 & { - 2}  \\   { - 1} & 0 & 1  \\ \end{array} } \right|
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  7. #7
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    Re: distance

    i get it to sqrt(17)/sqrt(3) is this wrong? it looks so for me :S
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  8. #8
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    Re: distance

    Quote Originally Posted by Petrus View Post
    i get it to sqrt(17)/sqrt(3) is this wrong? it looks so for me :S
    It is not what I get. What is D\times E~?
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  9. #9
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    Re: distance

    1i+2j+0k-(-1)k-1j-0i 1,1,1
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  10. #10
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    Re: distance

    Quote Originally Posted by Petrus View Post
    1i+2j+0k-(-1)k-1j-0i 1,1,1

    |(Q-P)\cdot(D\times E)|=3
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  11. #11
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    Re: distance

    Quote Originally Posted by Plato View Post
    |(Q-P)\cdot(D\times E)|=3
    is my D x E wrong? and how u get that to 3? im kinda confuse sorry but wanna ty u for helping me so far
    and that llD x Ell idk how u calculate with 2 absolutevalue if im going to be honest
    Last edited by Petrus; December 15th 2012 at 10:05 AM.
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  12. #12
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    Re: distance

    Quote Originally Posted by Petrus View Post
    is my D x E wrong? and how u get that to 3? im kinda confuse sorry but wanna ty u for helping me so far
    and that llD x Ell idk how u calculate with 2 absolutevalue if im going to be honest

    <-3,2,-2>\cdot <1,1,1>=~?
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  13. #13
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    Re: distance

    -3,2-2 then i take sqrt(-3^2+2^2+-2^2)?
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  14. #14
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    Re: distance

    Quote Originally Posted by Petrus View Post
    -3,2-2 then i take sqrt(-3^2+2^2+-2^2)?

    Sorry, I am done with this.
    You have absolutely no idea what any of this is about.
    Good luck.
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  15. #15
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    Re: distance

    i am really sorry i totaly agree with u but now i got it -3*1+2*1+-2*1 = -3 and sqrt(-3^2) = 3 but how do i do when its 2x absolute value :S? the answer shall be sqrt(2)
    btw that formula u gave me, where did u get it? what is the name of the formula :S? never seen it
    i get the answer 3/sqrt(3)
    Last edited by Petrus; December 15th 2012 at 11:29 AM.
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