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vector_components - Vector Components When you want to...

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Vector Components When you want to manipulate vectors, one of the most common ways is to use compo- nents. In two dimensions, we commonly use the symbols ˆ ı and ˆ to represent unit vectors (dimensionless) pointing along the x - and y -axes, then any other vector in the plane can be represented in terms of them as a sum such as F = F x ˆ ı + F y ˆ , where F x and F y are the two components of the vector F . Notice that the components are not themselves vectors! Because the unit vectors are at right angles to each other, it’s straight-forward to find the components of a vector by using a bit of trigonometry. If the picture is oriented in the way you expect, with the axes pointing left-right and up-down, it’s usually easy to find a right triangle and to use the definition of the sine and cosine to get the components. Often however, the picture isn’t set up the way you expect and you have to be more careful in finding the appropriate right triangle.
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