Question: Determine whether the following statements are true and give an explanation or counterexample.

1. \(pro{{j}_{\mathbf{v}}}\mathbf{u}=pro{{j}_{\mathbf{u}}}\mathbf{v}\)
2. If u is orthogonal to v and v is orthogonal to w, then u is orthogonal to w.
3. \({{\left( \mathbf{u}\cdot \mathbf{i} \right)}^{2}}+{{\left( \mathbf{u}\cdot \mathbf{j} \right)}^{2}}+{{\left( \mathbf{u}\cdot \mathbf{k} \right)}^{2}}=||\mathbf{u}|{{|}^{2}}\)
4. The cross product of two nonzero vectors is a nonzero vector.
5. Law of Cancellation? If u x v =u x w, then v = w?

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