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1) If u and v are orthogonal unit vectors, under what condition au+bv is orthogonal to...

1) If u and v are orthogonal unit vectors, under what condition au+bv is orthogonal to cu+dv (where a, b, c, d are scalars)? What are the lengths of those vectors (express them using a, b, c, d)?

2) Given two vectors u and v that are not orthogonal, prove that w=‖u‖2v−uuT v is orthogonal to u, where ‖x‖ is the L^2 norm of x.

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