Question

Find a vector parametric equation \vec{r}(t) for the line through the points P = \left(-5,4,-1\right) and Q = \left(-6,6,1\right) for each of the given conditions on the parameter t.

Answer 1

\[\begin{align*}\vec{r}(t)&=(1-t)\langle-5,4,-1\rangle+t\langle-6,6,1\rangle\\\\
&=\langle-5+5t,4-4t,-1+t\rangle+\langle-6t,6t,t\rangle\\\\
&=\langle-5-t,4+2t,-1+2t\rangle\end{align*}\]

Answer 2

what if they ask for r(6) and R(9?)

Answer 3

Plug in \(t=6\) and \(t-9\). These will give you coordinate points.