# If \vec{g} is in standard position with terminal point (5, 5) and \vec{h} is in standard position with terminal point (4, 2), how do you find the direction of the resultant vector?

Oct 24, 2014

$\setminus \vec{g} + \setminus \vec{h}$ is the resultant

$\setminus \vec{g} = 5 i + 5 j$
$\setminus \vec{h} = 4 i + 2 j$

So, resultant vector = $9 i + 7 j$ (From Triangle law of addition of vectors)

The vector is from (0,0) to (9,7) (Direction can also be determined from Triangle Law of addition of vectors)

To find the direction, slide the $\setminus \vec{h}$ parallelly from its position to the terminal point of the $\setminus \vec{g}$ (also called head of the vector) such that the tail of $\setminus \vec{h}$ (or starting point) of vector coincides with the head of $\setminus \vec{g}$. Now, the direction of resultant is from the tail of $\setminus \vec{g}$ to the head of $\setminus \vec{h}$.

The vectors will be something like below after sliding $\setminus \vec{h}$. Sorry, I couldn't find an image with $\setminus \vec{h}$ and $\setminus \vec{g}$. In the below image, $\setminus \vec{h}$ is similar to $\setminus \vec{B}$ and $\setminus \vec{g}$ is similar to $\setminus \vec{A}$.
$\setminus \vec{A} + \setminus \vec{B}$ is similar to $\setminus \vec{h} + \setminus \vec{g}$ Image Source : http://www.lnk2lrn.com/ap_physicssummer.html