Question: Let {v 1 , v 2 } be an orthogonal set of nonzero vectors, and let c 1 , c 2 be any nonzero scalars.

Let {v₁, v₂} be an orthogonal set of nonzero vectors, and let c₁, c₂ be any nonzero scalars. Show that {c₁v₁, c₂v₂} is also an orthogonal set. Since orthogonality of a set is defined in terms of pairs of vectors, this shows that if the vectors in an orthogonal set are normalized, the new set will still be orthogonal.

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