Euclidean vectors math to find coordinates for vector

[mimi.janson]

Homework Statement

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 can't 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 don't 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 don't 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

Homework Equations

The Attempt at a Solution

i have tried a lot of my formulas 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 don't really understand what to do about the minus .

 

[SammyS]

Homework Statement

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 can't 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 don't 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 don't 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

The Attempt at a Solution

i have tried a lot of my formulas 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 don't really understand what to do about the minus .

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, r_x, 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.

 

[mimi.janson]

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, r_x, 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.

yes thank you a lot