Vectors

Vectors as Order Pairs

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.
how to vector as ordered pair

In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis.

How to Solve ordered pair problems with vectors

Express the vector below as ordered pairs.

Practice Problem

Problem 6

Express the vector's coordinates below as ordered pairs in simplest radical form.

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: $$ ( \sqrt{3} , 2 ) $$

Problem 7

Express the vectors coordinates below as ordered pairs in simplest radical form.

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

Problem 8

Express the vectors coordinates below as ordered pairs in simplest radical form.

Vectors as ordered pair example
Problem 9

Express the vector below as ordered pairs.

vector in math problem
back to What is a Vector next to Resultant Vectors

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