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Math Help - Show that the two lines do not intersect.

  1. #1
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    Show that the two lines do not intersect.

    Hi all working through Anton and Busby.., if i have two vectors, v = (1,2,1)s and v = (9,6,0) + (0,1,-1)t how can i show that they do not intersect in 3-space ?
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  2. #2
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    By trying to find a point where they intersect! If these two lines intersected at (x, y, z), then we would have (x, y, z)= (s, 2s, s)= (9, 6+ t, -t) so we have s= 9, 2s= 6+ t, s= -t. Since the first equation tells you what s is, the third equation tells you what t must be. Do those values satisfy the second equation.
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  3. #3
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    HallsofIvy, thanks. it simplifies to 18 = -3. In this case would it be possible to find a line orthogonal to both lines? if so how can I find this. Thanks.
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  4. #4
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    Actually i think an orthogonal vector would just be n = (1,2,1)*(0,1,-1) = (0,2,-1). Would the vector then be x = (9,6,0) + (0,2,-1)t or would i need to omit the first point (9,6,0) ?
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  5. #5
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    The orthogonal to two vectors is cross product
    <br />
n = (1,2,1) \; \times \; (0,1,-1)=(-3,1,1).<br />
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