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In algebra-based courses, maybe this format is popular. Basically, you just give the magnitude of the vector and the angle from the positive x-axis that the vector is pointing. Here is an example using the same vector from before :. I am not too found of this format. First, if you want to add vectors, you need to find components.
Second, students often get confused with this angle always being measured from the same axis it doesn't have to be the x-axis, that is just what is common. Oh, if you want to do this for a 3-D vector, it really isn't worth it.
You would need two angles. Well, in some cases it might be worth it. With the component method, the idea is to just give the amount the vector is in each of the coordinate directions.
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Here is an example. Often you will see textbooks sort of stop here.
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In this case they may say something like:. The magnitude of a vector has to be a positive number. To really use these, you need unit vectors. This is what they look like:.
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A unit vector is a vector that has a magnitude of 1 with no units. This means that the F x vector could be written as:.
And maybe now you can see why that negative sign is important. The vector F x is in the opposite direction as the x-hat vector and that is why you need a negative sign. So, using this notation, you could write the vector F as:.
Same thing, different looks. Don't forget units though.
Vectors have units, if you leave them off you are probably a mathematician just kidding. Also, this notation can be expanded to three dimensions by adding a z-hat or k-hat component. Another nice thing is that these vectors are all set up and ready to add. If you have a vector in component notation you are ready to rock. I guess the reason textbooks use the magnitude-direction format some is that it may be easier to relate to real life. You cannot download or purchase for any new licenses.
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