# Vector Subtraction 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**, the **difference**, \(\alpha\)**v** - \(\beta\)**w** will be plotted in **red**, and (optionally) the **difference**, \(\beta\)**w** - \(\alpha\)**v** will be plotted in **purple**.

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