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Math Help - Equation of a line in R^3

  1. #1
    VkL
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    Equation of a line in R^3

    Find the equation of a line passing through points (2,4,-3) and (3,-1,1).

    How would I go about doing this?

    i understadn they are vectors, should I use matricies?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VkL View Post
    Find the equation of a line passing through points (2,4,-3) and (3,-1,1).

    How would I go about doing this?

    i understadn they are vectors, should I use matricies?
    1. Find a direction vector v =<a,b,c>

    2. Use the direction numbers a,b,c with one of your points to obtain a set of parametric equations.
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  3. #3
    VkL
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    I'm sorry, I don't mean to annoy, I do not understand.
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    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VkL View Post
    I'm sorry, I don't mean to annoy, I do not understand.
    That's okay.

    Direction vector: \vec{PQ}=<3-2,-1-4,1-(-3)>=<1,-5,4>=<a,b,c>

    So, the parametric representation of a line in 3 space is

    x=x_1+at, y=y_1+bt, and z=z_1+ct

    Finish up. If you get stuck, show me where.
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  5. #5
    VkL
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    would it be,

    x = 2 + t
    y = 4 -3t
    z = -3 + 4t

    ?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VkL View Post
    would it be,

    x = 2 + t
    y = 4 -5t
    z = -3 + 4t

    ?
    Correction, but yeah.
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  7. #7
    VkL
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    thank you very much!

    now if I want to find out where this line intersects the xZ-Plane, that would mean y = 0

    so I put,

    0 = 4 -5t

    t= (4/5)

    ? I am not sure, do I plug the t in to the other equations?
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  8. #8
    VkL
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    vectors*
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  9. #9
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VkL View Post
    thank you very much!

    now if I want to find out where this line intersects the xZ-Plane, that would mean y = 0

    so I put,

    0 = 4 -5t

    t= (4/5)

    ? I am not sure, do I plug the t in to the other equations?
    Well, sure because you need the other coordinates. IE Intersection point R: R(?,0,?)
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  10. #10
    VkL
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    right, thank you very much!
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  11. #11
    VkL
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    sorry again, If I am asked whether a certain point (x, y, z) lies on the line...I plug them into the vectors adn solve for t? and the t should be the same?
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  12. #12
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by VkL View Post
    sorry again, If I am asked whether a certain point (x, y, z) lies on the line...I plug them into the vectors adn solve for t? and the t should be the same?
    Indeed!
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  13. #13
    VkL
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    I keep messing up on this for some reason!

    Question is "decide if the lines l1 & l2 intersect or are skew or distinct..

    Just to make sure..

    Distinct means the parameter t is different for vectors x y and z ?
    parellel means that 1 vector has to be a scalar multipal of the other
    now skew means what??

    saw I find that line 1 and line 2 are not parallel
    example,

    L1: x = 1+t
    y = -2 + 3t
    z = 4 - t

    L2: x = 2t
    y = 3 + t
    z = -3 + 4t

    they are not parallel. now..

    what would setting the x = x y = y z = z tell me??
    setting
    1+t = 2t
    -2 + 3t = 3 + t
    4 - t = -3 + 4t


    Ok, say I solve the matrix, w.e... I get a value of t.. what does that value mean?
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  14. #14
    VkL
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    ?
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