9.5 - Lines in the Plane

Let $t$ be a scalar.

The vector $\myv r(t)=\myc{4,3}+t\myc{2,-1}$ is a function of $t$. Let $\myv r(t)$ be a position vector with its tail always at the origin.

Compute (and write down) the vectors $\myv r(t)$ for $t=$-1.5, -1, 0, 1, 2, and 3.

$\myv r(-1.5)=\langle 4,3\rangle -1.5\langle 2,-1\rangle= \langle 4,3\rangle +\langle -3,+1.5\rangle= $$\langle 1, 4.5\rangle$
$\myv r(-1)=\langle 2,4 \rangle$
$\myv r(0)=\langle 4,3 \rangle$
$\myv r(1)=\langle 6,2 \rangle$
$\myv r(2)=\langle 8,1 \rangle$
$\myv r(2)=\langle 10,0 \rangle$

Into the coordinate system below, draw the vectors $\myv r(t)$ for the values of $t$ you calculated above.

After plotting the position vectors, it looks like their tips all lie along a common line: