To GetReal, I say get real yourself. Please learn to post readable questions. It is only thanks to Prof. Ivy that I have any idea what you are asking.
In the post \(\displaystyle \vec{p}+\lambda_1\vec{u}+\lambda_2\vec{v}\) is a plane that contains the point \(\displaystyle p\) and is spanned be \(\displaystyle \vec{u}~\&~\vec{v}\).
Sadly I tell you that notation is arcane at best. Almost all modern textbooks would give the same plane as;
\(\displaystyle {<x,y,z>}\cdot(\vec{u}\times\vec{v})=\vec{p}\cdot(\vec{u}\times\vec{v}) \)