What do you mean by vector direction

Simple vector addition

Hello,

I can admit right at the beginning that I may be out of place here.
I'm taking a math exam tomorrow and get stuck with a "simple" vector addition problem - which could be due to a lack of basic knowledge of vectors.

I hope I can still be helped.

I have attached my task as a picture below.
As already mentioned: Until hours ago I had never had anything to do with vectors in my life, so please don't be surprised if my approach is completely wrong.

My approach:

vectora1 vectora2 = root (45² 30²
vectora3 vectora4 = root (37.5² 40²

wanted-end-vector.

Now there is my problem. In order to add up I would need the angles of the respective vectors.

You could calculate something using the sine law, à la:

sine (angle) sine ((105/180) * pi)

sine (angle) sine ((105/180) * pi))
Angle = arcsine sinus ((105/180) * pi))

With the angle I could then continue to calculate above.
Unfortunately, the whole thing always ends either in numbers that don't add up, or pocket calculator errors thanks to Winkel / Pi / translation errors on my part.



At this point I hope that one or the other has a lot to suggest to improve, if I still have specific questions:
Is my approach right or would it be wrong?
Is my approach suitable for such a task, or are there better solutions.
Help


'Simple vector addition' must be understood in a few hours
Unfortunately I have to be able to do that by tomorrow. I know, as I said, that I'm way too late, could be totally wrong here in the forum, but the learning plan wasn't different in terms of time. had a few other subjects and subjects.
Unfortunately, I am not the most talented math-book-formula-and-definitions-understander, so that I could neither learn how to proceed with such a task via math book nor Wikipedia.

With great hope for help,
Julia.

Thanks.


PS .: I apologize for the horrific formatting.


For everyone who wants to help me (automatically generated by OnlineMathe):
"I need a complete solution, please." (Assumes that the person asking the question adds all of his attempted solutions to the question and is actively involved in solving the problem.)Suitable for OnlineMathe:

Online exercises (exercises) at unterricht.de:
Hello,

first of all: You don't need a sine law. The normal trigonometric functions are sufficient to solve these vector traditions.

First introduce a coordinate system. The direction of the vector is best the x-direction (or how did you learn that? And a direction perpendicular to it is the y-direction (or

can you keep up that far?

lg josef
Unfortunately, I have to pass.
What exactly do you mean by "direction"?
If I had to answer the question "What is a vector", my answer would be "An arrow with a length and an angle." To date, I don't know more than these two characteristics.

Do you think one should imagine the vector as a straight line from the origin and now work with length on the x-axis and length on the y-axis?
Quasi: direction = root?
OK,
we are in one plane.

Because a vector has a direction and an angle in this plane, it can also be "divided" into two components (precisely these perpendicular directions.

so far clear?



Do you mean the vector with length root (2) and angle 45 ° can also be described as a straight line from the origin with x-distance / length and y-distance / length?
If not: Could you give me a specific numerical example of what you mean by that?
that's true. This is the Phythagoras (valid in a right-angled triangle with and as cathetuses standing at right angles to each other and a = hypothenose. Unfortunately, this has nothing to do with direction.
for the direction you need "sine" and "cosine" ;-)

Do you mean the vector with length root (2) and angle 45 ° can also be described as a straight line from the origin with x-distance / length and y-distance / length?
Right! Hopefully our texts won't cross over again.
Our texts do not cross each other
But your answers in my head.
In my opinion, I asked the same answer twice, but received two different answers. One time "no wrong, we now need sin / cos", one time "right".
Hehe.

I see it right:
One can also describe vectors in terms of distances or Pythagoras. However, this does not provide any information about the direction, only about the length.
Would that be responsible for statements about the direction of a vector?
Yeah just about.
Example:
Your vector would be. in component representation

The prerequisite is that the x-direction is to the right and the y-direction is up.
and also that, at least in thought, the origin of the coordinate system lies where all these "position vectors" have their starting point.
Well.
I just casually understood why exactly is in the unit circle at sine 1 and why it is smaller between up to degrees, as well as between and 0 degrees with the same amount.

How do I get from my vector,. to determine a direction from the and lengths of my vector? What does such a direction look like anyway? Is that a number? Is it two numbers and?

And then: Do I just add the directions of the individual vectors in order to have the direction of the end vector, or how would that work?
It's nice when you have seen through the connections in the unit circle.

Unfortunately, my answer with the components has now been lost.

Here again differently:

If you have created the vector components as I showed you above, then you have already "processed" the vector direction. Ie. it is already included in the vector components and you do not need to worry about it any further. So you have your "back free again" and can finally start the Vekroraddition.

Incidentally, there is unfortunately for 75 ° no "nice" equivalent in radians See also

http // de.wikipedia.org / wiki / Formula Collection_Trigonometrie # important% 20 function values


"How do I come from my vector, from the and lengths of my vector to determine a direction? What does such a direction look like? Is that a number?"
The direction is something that, as I said, is contained in the vector components.
and vectors are added by adding their components.

The direction of is given in your task and simply the angle 75 °
The amount of is and is also given in your task

"Is it two numbers and y)?"
The two components contain the amount and direction of the vector. But for this you need a coordinate system, which you introduce first (see also task)
a-sum-y = sin (0 °) * 45 sin (75 °) * 30 sin (120 °) * 37.5 sin (225 °) * 40
a-sum-x = cos (0 °) * 45 cos (75 °) * 30 cos (120 °) * 37.5 cos (225 °) * 40

a-sum
a-sum


a-sum length = root


So?

// edited
Well, if the x-direction goes from the origin to the right, then I believe that the x-component of each vector is
(with as defined in the unit circle)
should be.
Correspondingly, if the y-direction “points upwards perpendicular to it”, the y-component of each vector is
(with as defined in the unit circle)
otherwise it doesn't look so bad for the length of the result vector ;-)
What do you mean by "alpha as defined in the unit circle"?
In the unit circle I only know the revolutions of it, or stop conversion (90 ° / 180 °).

And I get the corresponding angle via:

180°

right?

// edited
do you have my answer by o'clock,
read?
Yes I have.
then why do you write "sinus" for the x-direction?
OK. I have read your answer, but only now do I realize what you mean by that. Here in the bib it feels like 400 °.
Excuse me. Editiers the same. My mistake
Well.
180°

Now fits the angle, right?
well I believe that in your account of clock,
the two directions and reversed. Look again at my answer from Uhr
I wasn't even at the angle ("in" my thoughts).
At the end I would draw the result vector in the coordinate system (which you introduced at the very beginning (see note in the exercise), and thus check the angle that comes from your formula.


Since I only have a short time left:
If you have not miscalculated, the result vector should be the following:
(I used your numerical values)
This gives a length of
how you got it out correctly about Phythagoras.

The angle between the x-direction and is less than 90 ° (from the drawing solution via "forces parallelogram")
arcsin and is about 80 °
but what would be nicer to calculate like this:
arctan

I'm just sitting there trying to understand. Errors caused by little things keep coming in - maths ;-)
If you're gone before I made it: Thank you very much. Has brought me a lot either way.
always happy :-)
ideally the next time with a slightly longer time interval to exams. ;-)
lg josef
oh yes, one more addendum:
Maybe it was just a mistake on your part, but you should in your answer from
Clock,
still in the formula that
Replace "" with "arccos".
Reason: you always get to the angle (regardless of whether in radians or degrees) with the inverse function of the angle function, in this case with the arc cosine.
As you write it in this formula, your calculator must be set to "RAD" so that the result comes out "in radians". The "divide by" and the "multiply by 180 °" indicate this ;-)
On the other hand, you can save yourself this "detour" if you have calculated everything in degrees (your pocket calculator works in "DEG" anyway, as your results from above show ;-)
"Radians" make the task easier when "nice" angles appear like in my Wikipedia link from Uhr. There are then in particular exact numerical values ​​such as
e.g. For
In these cases you should always have a corresponding table available.
But there are also tasks that you always have to work on in radians. Unfortunately, I can't think of a suitable example at the moment.
The "circumference" of the unit circle piece from 0 to the angle in rad (radian measure) is nothing else than the "radian measure", perhaps this name will also become clearer to you.
lg josef


This question was automatically closed because the person who asked the question no longer showed any interest in the question.