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Using Mathematica for parallelogram law

Anonymous User
Anonymous User
Posted 10 years ago

How would you use Mathematica to verify the parallelogram law in real numbers^3 for any pair of vectors u and v.

POSTED BY: Anonymous User
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This is pretty much the same as David's answer but done using Grassmann algebra. The only real advantage here is a more transparent geometric language. The generation of the two sides are done with ComposeVector commands that generate generic vectors in the space.

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The GrassmannCalculus Application is developmental but fairly far along. Anyone interested in exploring Grassmann algebra with it may contact me.

In two dimensions:

v1 = {a, b};
v2 = {c, d}

Expand[2 Tr[v1^2] + 2 Tr[v2^2] == Tr[(v1 + v2)^2] + Tr[(v1 - v2)^2]]

In three dimensions:

v1 = {a, b, c};
v2 = {d, e, f};

Expand[2 Tr[v1^2] + 2 Tr[v2^2] == Tr[(v1 + v2)^2] + Tr[(v1 - v2)^2]]
POSTED BY: David Reiss
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