Co-planar Vectors

2+ vectors that span the same plane in $R^3$ These vectors will share the same $R^2$ space

Proving Coplanarity

If you have 2 vectors $\vec{a},\vec{b}$, they are ALWAYS coplanar. If you have 3 vectors $\vec{a},\vec{b},\vec{c}$, you must prove that they are all coplanar to eachother

Triple Product Method

If $\vec{a}\times \vec{b}$ is colinear with $\vec{b}\times \vec{c}$ then $\vec{a},\vec{b},\vec{c}$ are coplanar. $\vec{a}\cdot (\vec{b}\times \vec{c})=0$

Algebraic Method

You can write one vector as a linear combination of the other 2. $\vec{a}=s\vec{b}+t\vec{c}$