# Euclidean vectors math to find coordinates for vector

1. Dec 29, 2011

### mimi.janson

1. The problem statement, all variables and given/known data

I have this question about Euclidean vectors.
in a coordinate system vector r and s and t are given . (there is an arrow on top of r, s and t but i cant put it in
l r l is 3,48 and creates an angle of 44,3 degrees with x (x is a straight horizontal line)
l s l is 4,16 and creates an angle of 116,8 degrees with x
l t l is 6,16 and creates an angle of 321,6 degrees with x

FIRST question )
Find out what the coordinates for vector r-s+t are ??? i know that the answer must be

(9,19
-5,11)
But i dont really know how i can get the result step by step

SECOND question)
Find l r-s+t l (there is arrow on r,s,t again so here they ask about the length)
the result must be (10,52) but again ...i dont know how to show it and calculate it step by step

THIRD question)
i have to find the angle that r-s+t creates with the x- axe but the result has to be 330,92 and i cannot understand this too since i get the wrong result

so if anyone is nice and clever PLEASE help me understand how you can solve these three questions step by step

2. Relevant equations

3. The attempt at a solution
i have tried alot of my formulars to understand it but it seems like you have to mix them together which is the hard part to understand .

if it was only plus i know that i had to use the cos relation
a2= b2+c2- 2*a*b*cosA
but i think something is wrong because i dont really understand what to do about the minus .

2. Dec 29, 2011

### SammyS

Staff Emeritus
First of all: If you can't put an arrow above the symbol, it's common to put vectors in bold font.

Also, many who use this Forum, use a decimal point ' . 'rather than a comma ' , ' .

I assume the specified angles are counter-clockwise (anti-clockwise) with respect to the positive x-axis.

To find the x component, rx, of vector, r, if it makes an angle of θ w.r.t. the +x-axis, use:
$r_x=|\vec{r}|\cos(\theta)\,.$​

Similarly, the y component is given by:
$r_y=|\vec{r}|\sin(\theta)\,.$​

That should get you started.

3. Jan 29, 2012

### mimi.janson

yes thank you alot