Recently, i was talking around vectors. At the time, I had actually to stop and recall how I had been representing vectors. Ideally, I have to stick v the same notation I supplied in Basics: Vectors and also Vector Addition. Yet let me go over the different ways you could represent a vector.

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Maybe this is as well obvious, however it had to it is in said. You can represent vectors by drawing them. In fact, this is really useful conceptually - but maybe no too valuable for calculations. Once a vector is represented graphically, its size is stood for by the length of an arrow and also its direction is stood for by the direction the the arrow. Right here is one example:

I think the biggest an unfavorable to this depiction (other than being an overwhelming to acquire numerical answers for adding) is that it is no too basic to stand for in 3-dimensions. Because that the adhering to representations, i will try to said them come the graphical representation.

In algebra-based courses, probably this layout is popular. Basically, friend just offer the magnitude of the vector and the edge (from the hopeful x-axis) that the vector is pointing. Below is an instance (using the very same vector indigenous before):

I am no too uncovered of this format. First, if you desire to add vectors, you require to find components. Second, students regularly get confused with this angle constantly being measured indigenous the same axis (it doesn't have to be the x-axis, that is simply what is common). Oh, if you desire to perform this for a 3-D vector, it yes, really isn't worth it. You would require two angles. Well, in some cases it can be precious it.

With the component method, the idea is to just provide the quantity the vector is in every of the name: coordinates directions. Right here is one example.

Hold on. I am not finished. Yes, I wrote these materials as vectors so that:

Often girlfriend will watch textbooks type of protect against here. In this case they might say miscellaneous like:

It is important to realize that this notation is not the size of the vector Fx and Fy. The magnitude of a vector has to be a hopeful number. To really usage these, you need unit vectors. This is what they look like:

The tiny x^ over the x means that that is a unit vector. A unit vector is a vector that has a magnitude of 1 v no units. This way that the Fx vector can be created as:

And maybe currently you deserve to see why that an unfavorable sign is important. The vector Fx is in opposing direction together the x-hat vector and that is why you need a an adverse sign. So, making use of this notation, you might write the vector F as:

Some textbooks prefer the you i, and j rather of x and y - this would look like:

Same thing, various looks. Don't forget systems though. Vectors have actually units, if you leaving them turn off you are more than likely a mathematician (just kidding). Also, this notation can be broadened to three dimensions by adding a z-hat or k-hat component. Another nice point is that these vectors room all set up and ready to add. If you have actually a vector in component notation you are prepared to rock.

I guess: v the factor textbooks usage the magnitude-direction format some is the it might be easier to called to real life. In actual life, I would certainly measure the magnitude and also direction the a force and then have to calculate the components.

Same thing, but an additional way

I really prefer the physics textbook Matter and also Interactions through Ruth Chabay and Bruce Sherwood. The means that textbook repeatedly represents vectors is as:

I like this notation. It is short and it emphasizes the components and also the idea the all forces are 3-dimensional. The quick thing is really great for lazy civilization like me. Also, that matches up really nicely through vectors in vpython. Right here is just how I would certainly write the vector in vpython:

Rhett Allain is an combine professor the physics at Southeastern Louisiana University. That enjoys teaching and also talking around physics. Occasionally he takes things apart and can't placed them earlier together.

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