1. ## 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?

2. Originally Posted by Monster32432421
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.

3. Originally Posted by HallsofIvy
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