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# Vector pyramid watch

1. The picture shows a pyramid with a square base B,C,D,E. Let

x=AC u=CB v=DC w=AE

Give a formula for x in terms of u, v and w.

Can anyone help me with this?
2. When you add together vectors, you can consider this as taking a route along a path, and it's only your starting point and destination that matter. For example, in this pyramid, AB is the same AE + EB, because you've taken a path between points and started and finished at the same place. Therefore, AB = AE + EB. We could derive several other results.

Also, because BE and CD are parallel, going in the same direction, and are of the same length, we can say that EB = DC (= v), and similarly CB = DE (= u).

A final rule is that you can reverse the direction of a vector by making it negative, e.g. AB = -BA.

Now, x = AC. Can you, using these facts and rules, find another "path" from A to C in terms of the vectors u, v and w?

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Updated: November 11, 2008
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