Sketch the plane given by 2x+y+3z=6

How is this done?

Note: I have the answer for this and can see it is a traingle shaped guy in a 3d...

I have no clue how to do these without a calculator or answer key in front of me.

Please advise.

Thanks!

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- Aug 5th 2009, 09:01 PMorendaclsketching planes?
Sketch the plane given by 2x+y+3z=6

How is this done?

Note: I have the answer for this and can see it is a traingle shaped guy in a 3d...

I have no clue how to do these without a calculator or answer key in front of me.

Please advise.

Thanks! - Aug 5th 2009, 09:45 PMearboth
This is one possible method:

1. Calculate the coordinates of the points of intersection between the plane and the coordinate axes. For instance: The x-axis crosses the plane if y = 0 and z = 0, thus $\displaystyle P_x(3,0,0)$, etc.

2. Draw the 3 axes and the intersection points. You'll get a triangle which defines the plane in 3D. The sides of the triangle are the intersections between the given plane and the coordinate planes.

(Remark: I used isometric paper whose axes include an angle of 120°)