How to express a vector as an ordered pais
- Follow these steps
- Align the 'tail' of the vector with the origin
- Determine the x and y coordinates where the head or 'pointy end' of the vector lands. Typically, for this you need to use sine and cosine ratios.
In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis.
Express the vector below as ordered pairs.
Practice Problem
x coordinate
$$
= 2 \cdot { \bf cos}(30^{\circ})
\\
= 2 \cdot \frac{\sqrt{3}}{2}= \sqrt{3}
$$
y coordinate
$$
= 2 \cdot { \bf sin}(30^{\circ})
\\
= 2 \cdot \frac{1}{2}=2
$$
Ordered Pair: $$ ( \sqrt{3} , 2 ) $$
This was kind of a trick question in that you must recognize that the 60° angle is the same as the prior problem's angle.
x coordinate = 2 ×sin(60°) = 
y coordinate = 2 ×cos(60°) = 2(½) = 1
