Solving an linear system

[hkus10]

1) Find a vector equation for the plane in R3(3D) with scalar equation 2x − 3y + z = 5 .

 

First,I find three points on the plane and then I used one point as a fixed point in order to find two vectors on the plane by using two other points. Then, I tried to test whether the two vectors are perpendicular to the normal vector of this plane by using cross product. However, I do not get the right normal vector by using my two vectors on the plane?

My question is that whether my approach is wrong? If yes, what should I do?

Edited February 26, 2011 by hkus10

[the tree]

Then, I tried to test whether the two vectors are perpendicular to the normal vector of this plane by using cross product. However, I do not get the right normal vector by using my two vectors on the plane?

I'm a little confused here: if you're testing your normal using the cross product, then how are you finding it in the first place? A cross product of any two vectors vectors on the plane should give a perfectly good normal vector.