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Math Help - parallel

  1. #1
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    parallel

    which of the following lines is parallel to the plane 4x+y-z-10=0

    a) \vec{r}=(3,0,2)+t(1,-2,2)


    b) x=-3t,y=-5+2t,z=-10t


    c) \frac{x-1}{4}=\frac{y+6}{-1}=\frac{z}{1}
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  2. #2
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    A line is parallel to a plane if and only if the direction of the line is perpendicular to the normal of the plane.
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  3. #3
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    Quote Originally Posted by Plato View Post
    A line is parallel to a plane if and only if the direction of the line is perpendicular to the normal of the plane.
    i know the normal is (4,1,-1) although i'm not sure if i know what you mean by direction of the line
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  4. #4
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    Quote Originally Posted by william View Post
    which of the following lines is parallel to the plane 4x+y-z-10=0

    a) \vec{r}=(3,0,2)+t(1,-2,2) the direction vector is \color{red}<1,-2,2>


    b) x=-3t,y=-5+2t,z=-10t the direction vector is \color{red}<-3,2,-10>


    c) \frac{x-1}{4}=\frac{y+6}{-1}=\frac{z}{1} the direction vector is \color{red}<4,-1,1>
    .
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  5. #5
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    Quote Originally Posted by Plato View Post
    .
    i'm sorry im still really stumped are you saying the the third one would be parallel to the plane? wouldn't it have to be <-4,-1,1> Note* the back of my book says the second and only the second like is parallel to the plane. Also, how would i determine if any of the lines lies in the plane.
    Last edited by william; March 11th 2010 at 12:46 PM.
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  6. #6
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    No, neither <4, -1, 1>.<4, 1, -1> nor <-4, -1, 1>.<4, 1, -1> is equal to 0.


    What is <1, -2, 2>.<4, 1, -1>?

    What is <-3, 2, -10>.<4, 1, -1>?

    A line lies in the plane if and only if (x, y, z) satisifes the equation of the plane for all t. That is, put the expressions for x, y, and z in the line, in terms of t, into the equation of the plane. If the entire line is in the plane, the "t" terms will cancel out, giving a equation that is always true, like "0 = 0". If a line is parallel to the plane but not in it, the "t" terms will also cancel but give an equation that is always false, like "1= 0".
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  7. #7
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    Quote Originally Posted by HallsofIvy View Post
    No, neither <4, -1, 1>.<4, 1, -1> nor <-4, -1, 1>.<4, 1, -1> is equal to 0.


    What is <1, -2, 2>.<4, 1, -1>?

    What is <-3, 2, -10>.<4, 1, -1>?

    A line lies in the plane if and only if (x, y, z) satisifes the equation of the plane for all t. That is, put the expressions for x, y, and z in the line, in terms of t, into the equation of the plane. If the entire line is in the plane, the "t" terms will cancel out, giving a equation that is always true, like "0 = 0". If a line is parallel to the plane but not in it, the "t" terms will also cancel but give an equation that is always false, like "1= 0".
    THANK YOU!!!! this makes it much, much more clear!

    must be line 2
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