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).