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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- Apr 13th 2010, 05:00 AMMonster32432421Sketching 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? - Apr 13th 2010, 05:35 AMHallsofIvy
When $\displaystyle \lambda_1=\lambda_2= 0$ we get (0, 3, -1). When $\displaystyle \lambda_1= 0$ and $\displaystyle \lambda_2= 1$ we get (0, 3, -1)+ (3, -1, 1)= (3, 2, 0). When $\displaystyle \lambda_1= \lambda_2= 1$ 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. - Apr 13th 2010, 05:38 AMMonster32432421