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Math Help - Vector line equations

  1. #1
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    Vector line equations

    I've done the first part of the attached question. 6lambda:1mu.

    I don't think the hints make sense. c is perpendicular to a. How can it be on a plane with a and b and also be parallel to l as implied by r=a+kc?
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  2. #2
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    c is not parallel to l. r = a + kc means that each point of l is a resultant of a and some vector collinear with c. This is guaranteed becase a and c form a basis for the plane that l lies in.
    This is akin to the vector equation of a line with standard basis: r = b + kx.
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  3. #3
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    Quote Originally Posted by Stuck Man View Post
    I don't think the hints make sense. c is perpendicular to a. How can it be on a plane with a and b and also be parallel to l as implied by r=a+kc?
    The vector a\times(a\times b)=(a\cdot b)a-(a\cdot a)b is clearly perpendicular to a and as a linear combination of a~\&~b it is in the plane of a~,~b,~&~O.
    Now you can finish?
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  4. #4
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    Here is what you cannot read
    The vector a x (a x b)=(a.b)a-(a.a)b is clearly perpendicular to a and as a linear combination of a~\&~b it is in the plane of a~,~b,~\&~O.
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  5. #5
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    Here is what you cannot read
    The vector a x (a x b)=(a.b)a-(a.a)b is clearly perpendicular to a and as a linear combination of a~\&~b it is in the plane of a, b, & O.
    Last edited by Plato; June 17th 2010 at 03:28 PM.
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  6. #6
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    Quote Originally Posted by slider142 View Post
    c is not parallel to l. r = a + kc means that each point of l is a resultant of a and some vector collinear with c.
    My book says "The equation of a straight line parallel to vector b through a point with position vector a is r=a+tb." That is why I thought the line l would be parallel to c.
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  7. #7
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    I have consulted another source which was helpful and can confirm that you are wrong slider142.

    I had been thinking that c is a position vector so I can understand it all better now. slider142 also seems to have thought that c is a position vector.

    I calculated that lambda:mu is 6:1 but the book says 1:6. Is the book wrong? I think I can do all the rest of the question.
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  8. #8
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    After 3 days still no one has given me any help.

    Why is lambda:mu 1:6? Is the equation of line l r=i-2j+k+t(13i+4j-5k) as the book says? Why is p=-12i-6j+6k? Why is p not equal to b?
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  9. #9
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    I've finally done the question. Line l actually meets OB produced.
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