Prove if it's true or false that there is a plane constructed using the dots (0,5,3), (1,-2,4) and (-1/2, 8,0).
My approximation is this:
Parameterize the equation of the plane taking (0,5,3) as the translate vector, so:
$P = (0,5,3) + r(1,-7,1) + s(-11/2, 3, 0)$
Now, given that both direction vectors r and s are non parallel then they form a basis for the 2-flat and so it is true there is a plane constructed using the dots. Is as this as simple?