# Vectors and Planes

• January 2nd 2008, 05:23 AM
geordieman1011
Vectors and Planes
I have 3 points A,B and C, with coordinates (0,1,1) (-2,-1,-5) and (1,-1,0)
I have found vectors AB and AC, the found the equation of the plane ABC as
r= (0,1,1) + λ(-2,-2,-6) + μ(1,-2,-1). the brackets in the 'r=' formula are vertical brackets. I am having trouble verifying that A,B and C lie in the plane
5x + 4y - 3z = 1
• January 2nd 2008, 06:01 AM
Soroban
Hello, geordieman1011!

Quote:

I have 3 points: . $A(0,1,1),\;B(-2,-1,-5),\;C(1,-1,0)$
I am having trouble verifying that A, B and C lie in the plane: $5x + 4y - 3z \:= \:1$
. . . Really?

If a point lies in a plane, its coordinates satisfy the equation of the plane.
. . . . . basic stuff!

It's like asking: How do I know that $(4,-1)$ is on $2x + 3y \:=\:5$ ?

• January 2nd 2008, 06:09 AM
geordieman1011
thanx for pointing that out for me, my brain wasn't fully switched on