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Basis vectors

http://www.vitutor.com/geometry/vectors/basis_vector.html

Hey, could someone please explain the method behind the second part of the first example where they determine the new co ordinates of the vector with the basis.

I don't get how they can just add x, y and z before the basis vectors and that turns out to be the new x y and z co ordinates? Would it matter if we switched the order of the x y and z?
Reply 1
Because it's a new basis, where the u vector denotes the equivelant of the x direction, the v vector denotes the equivelant of the y direction and the w vector denotes the equivelant of the z direction. So multiplying x by the u vector, y by the v vector and z by the w vector and adding the vectors together will give you another vector which will tell you the coordinates in the new basis when you sub in x y and z coordinates. Think i may have explained quite badly but maybe read up more on basis vectors to understand what they are etc
(edited 9 years ago)

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