# Vector Addition and Scalar Multiplication

## An interactive 3D plot

You can specify two vectors **v** and **w** (as well as a base point, P, if you wish, which will be common to both vectors). You may also multiply **v** by a scalar \(\alpha\) and **w** by a scalar \(\beta\) by adjusting the sliders (by default \(\alpha\) and \(\beta\) are set to 1). The vector \(\alpha\)**v** will be plotted in blue, \(\beta\)**w** will be plotted in green, and their **sum**, \(\alpha\)v + \(\beta\)**w** will be plotted in red. Optionally, you can view the the vectors **v, w** translated to form a parallelogram.

Click the "Evaluate" button below to view and calculate vector sums (the actual Sage code is included in the box only in case you're interested; you don't need to modify the code).