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Math Help - Sketching a plane

  1. #1
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    Sketching a plane

    S={x∈R^3|x= (0,3,-1) + λ1(1,2,1) + λ2(3,-1,1) for 0≤ λ1≤1 and λ1 ≤ λ2≤1}

    Sketch S, labelling all important points..


    Could someone show me how I would do this and suggest an online program which would sketch things like these?
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  2. #2
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    Quote Originally Posted by Monster32432421 View Post
    S={x∈R^3|x= (0,3,-1) + λ1(1,2,1) + λ2(3,-1,1) for 0≤ λ1≤1 and λ1 ≤ λ2≤1}

    Sketch S, labelling all important points..


    Could someone show me how I would do this and suggest an online program which would sketch things like these?
    When \lambda_1=\lambda_2= 0 we get (0, 3, -1). When \lambda_1= 0 and \lambda_2= 1 we get (0, 3, -1)+ (3, -1, 1)= (3, 2, 0). When \lambda_1= \lambda_2= 1 we get (0, 3, -1)+ (1, 2, 1)+ (3, -1, 1)= (4, 4, 1).

    Mark those three points on a coordinate system. You plane is the unique plane that contains all three points.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    When \lambda_1=\lambda_2= 0 we get (0, 3, -1). When \lambda_1= 0 and \lambda_2= 1 we get (0, 3, -1)+ (3, -1, 1)= (3, 2, 0). When \lambda_1= \lambda_2= 1 we get (0, 3, -1)+ (1, 2, 1)+ (3, -1, 1)= (4, 4, 1).

    Mark those three points on a coordinate system. You plane is the unique plane that contains all three points.
    How come you sub in λ1 =0 and λ2= 1?
    cause when I did it.. I put in λ1=1, λ2=-1.. would I still be correct
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