Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
Home Newtonian Physics Vectors Techniques for Adding Vectors  
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Techniques for Adding VectorsAddition of vectors given their components The easiest type of vector addition is when you are in possession of the components, and want to find the components of their sum.
Addition of vectors given their magnitudes and directionsIn this case, you must first translate the magnitudes and directions into components, and the add the components.
Graphical addition of vectorsOften the easiest way to add vectors is by making a scale drawing on a piece of paper. This is known as graphical addition, as opposed to the analytic techniques discussed previously.
Even when we don't intend to do an actual graphical calculation with a ruler and protractor, it can be convenient to diagram the addition of vectors in this way. With Δr vectors, it intuitively makes sense to lay the vectors tiptotail and draw the sum vector from the tail of the first vector to the tip of the second vector. We can do the same when adding other vectors such as force vectors.
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