Suppose we want to express a vector
in terms of components perpendicular and parallel to some other vector
We can peg the vectors to the origin.
If the angle between them is
where
is the anticlockwise direction from
to
we can write the direction vector ofas
The component ofin the direction ofis then
To find the component ofperpendicular to
draw in the perpendicular toas shown below.
The component ofin the direction perpendicular tois then
If
take the negative square root and if
take the positive square root.
Example: Find the components of
perpendicular and parallel to
