# Sketching a plane

• Apr 13th 2010, 05:00 AM
Monster32432421
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?
• Apr 13th 2010, 05:35 AM
HallsofIvy
Quote:

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 $\displaystyle \lambda_1=\lambda_2= 0$ 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 AM
Monster32432421
Quote:

Originally Posted by HallsofIvy
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.

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