What do you mean by vector direction
Simple vector addition
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.
vectora1 vectora2 = root (45² 30²
vectora3 vectora4 = root (37.5² 40²
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.
'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,
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.)
Online exercises (exercises) at unterricht.de:
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?
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?
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?
If not: Could you give me a specific numerical example of what you mean by that?
for the direction you need "sine" and "cosine" ;-)
Right! Hopefully our texts won't cross over again.
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".
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?
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.
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?
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
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-x = cos (0 °) * 45 cos (75 °) * 30 cos (120 °) * 37.5 cos (225 °) * 40
a-sum length = root
(with as defined in the unit circle)
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 ;-)
In the unit circle I only know the revolutions of it, or stop conversion (90 ° / 180 °).
And I get the corresponding angle via:
Excuse me. Editiers the same. My mistake
Now fits the angle, right?
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.
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:
If you're gone before I made it: Thank you very much. Has brought me a lot either way.
ideally the next time with a slightly longer time interval to exams. ;-)
Maybe it was just a mistake on your part, but you should in your answer from
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
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.
This question was automatically closed because the person who asked the question no longer showed any interest in the question.
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