Question

will award medal
Find a vector equation and parametric equations for the line segment that joins P to Q.P<1,0,1>
Q<5,3,1>

Answer 1

@ ganeshie8

Answer 2

@ganeshie8

Answer 3

so the equation for a paremetric equation you designate r_0 and r_1. does it make a difference which one is which. or the left most one needs to be r_0?

Answer 4

@SithsAndGiggles

Answer 5

The order does matter. \(\vec{PQ}\) points in the opposite direction as \(\vec{QP}\).

Answer 6

Typically, line segments are parameterized using the following form
\[\vec{PQ}:\quad\vec{r}(t)=(1-t)\vec{P}+t\vec{Q}\]
with real \(t\) ranging from \(0\) to \(1\). Notice that
\[\vec{r}(0)=\vec{P}\\
\vec{r}(1)=\vec{Q}\]

Answer 7

In some cases, like horizontal or vertical line segments, you can use "simpler" parameterizations. For example, if \(\vec{P}=\langle0,0,0\rangle\) and \(\vec{Q}=\langle2,0,0\rangle\), you can parameterize \(\vec{PQ}\) with
\[\vec{r}(t)=\langle t,0,0\rangle\]
with \(0\le t\le2\).