# 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).