Question

How would you write a vector equation for a line using parametric equations? For example:

A line is defined by x=-2-t and y=4+2t,teR. a) Write a vector equation for this line using parametric equations.
b) write a second vector equation different from the first

Answer 1

Also, R(-9,18) lies on the line

Answer 2

The vector equation for the line is

<b>r</b>(t) = x(t) <b>i</b> + y(t) <b>j</b>
= (-2-t)<b>i</b> + (4+2t)<b>j</b>

<b>r</b>(0) = -2<b>i</b>+4<b>j</b>
<b>r</b>(t) = -2<b>i</b>+4<b>j</b> + t(-<b>i</b>+2<b>j</b>)