# 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).