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).