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....

Techniques for Adding Vectors

Addition 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.

Adding components.

Addition of vectors given their magnitudes and directions

In this case, you must first translate the magnitudes and directions into components, and the add the components.

Graphical addition of vectors

Often 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.

LA to Vegas, graphically.

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 tip-to-tail 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.

f / Vectors can be added graphically by placing them tip to tail, and then drawing a vector from the tail of the first vector to the tip of the second vector.

Self-Check How would you subtract vectors graphically?
Answer A-B is equivalent to A+(-B), which can be calculated graphically by reversing B to form -B, and then adding it to A.

Discussion Questions

A If you're doing graphical addition of vectors, does it matter which vector you start with and which vector you start from the other vector's tip?
B If you add a vector with magnitude 1 to a vector of magnitude 2, what magnitudes are possible for the vector sum?
C Which of these examples of vector addition are correct, and which are incorrect?

Last Update: 2010-11-11