Vector Algebra

a point on the third side of a triangle for which $\mathbf{a}, \mathbf{b}$ are two sides, only when $0 \leq t \leq 1$

a point on the line joining the points whose position vectors are $\mathbf{a}$ and $\mathbf{b}$

a vector in the plane of $\mathbf{a}, \mathbf{b}$ only whent $>1$

a vector in the plane parallel to the plane of $\mathbf{a}$ and $\mathbf{b}$, only when $-1 \leq t \leq 1$