Linear Combinations of Two Vectors
Vector Sandbox
Directions:
At any time, you may reset the applet by pressing the refresh symbol in the top right. You can zoom out the applet by using your scroll wheel on your mouse inside the applet. You can drag inside the applet to see more to each side as well.
Task 1:
You must use the given vectors and . The only things that you can adjust are the weights and by moving the sliders left and right.
(a) What weights can we choose so that is the zero vector?
(b) Are your weights from (a) unique, or are there other choices? If there are other choices, what is another choice?
Task 2:
Now you may choose your own vectors and by sliding the blue and green vertices, respectively. You can also still adjust the weights and by moving the sliders left and right.
(c) Give an example of a linear combination that resulted in the zero vector that did not have 0's for the weights.
(d) What is interesting about your vectors and from (c)?