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Show that ( vec a- vec b)xx( vec a+ vec ...

Show that `( vec a- vec b)xx( vec a+ vec b)=2 vec axx vec b` and given a geometrical interpretation of it.

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`(veca - vecb) xx (veca + vecb) `
`= vecaxxveca + vecaxxvecb -vecbxxveca -vecbxxvecb`
`= veca xx veca + veca xx vecb + veca xx vecb -vecb xx vecb`
`= vec0 + 2veca xx vecb - vec0 = 2vea xx vecb`
Geometrically, the vector area of a parallelogram, whose sides are along vectors, `veca and vecb is veca xx vecb`. Also diagonals are long vectors, `veca - vecb and veca + vecb` and the vector area in terms of diagonal vectors is
`1/2 [(veca -vecb) xx (veca + vecb)]`
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