Linear combination

Instructions

First, move the two blue points whose default locations are

and

. These points determine the vectors

and

. Notice as you do this the light blue lines move. The intersections of blue lines show terminal points of the linear combination

for integer values of

and

. The vector

is depicted in black, and you can change the values of

and

using the purple sliders. A purple parallelogram shows the geometric depiction of adding the vector

and the vector