This applet is designed to build intuition about the subspace of R3
defined as the set of linear combinations of two given vectors.
The applet has a control window and a graphics windows called
The vectors U, V, and W are entered in the control window as
Scalars a and b are scrollable with the vcr buttons. Values
can also be typed in for these constants. The value CoeffientMax
gives the maximum magnitude for these scalars.
The value zoomFactor gives the scale of the axes.
Things to notice:
A checkbox lets you add in the subspace of linear combinations of
U and V.
The vector W can be entered directly to see if it is in the space
of linear combinations of U and V. To see if W is a linear
combination of U and V, rotate the vectors window so you are looking at
the plane from the side.
A readout gives the coordinates of the linear combination a*U+b*V.