Vector Equation of a Plane

• From point $P$, we walk $s$ units in the $\vec{u}$ direction and then turn to the $\vec{v}$ direction and walk $t$ units in that direction.
• This traces out a two-dimensional figure, which, when extended infinitely, gives us a plane.

$$\vec{x}=\left[\begin{array}{c}{x}_1\\ x_2\\ .\\ .\\ x_n\end{array}\right]=\vec{p}+s\vec{u}+t\vec{v}$$

• This expression gives us the vector $\vec{x}$ in $R^n$. We can break this down for each $R$ to give us the Parametric Equation of a Plane.

$${\vec{x}}_n=={\vec{p}}_n+s{\vec{u}}_n+t{\vec{v}}_n$$