Group Activity Express each vector in component form and prove the following properties
Chapter 6, Problem 6.1.1.64(choose chapter or problem)
Group Activity Express each vector in component form and prove the following properties of vectors.
(a) \(\mathbf{u}+\mathbf{v}=\mathbf{v}+\mathbf{u} \)
(b) \((\mathbf{u}+\mathbf{v})+\mathbf{w}=\mathbf{u}+(\mathbf{v}+\mathbf{w}) \)
(c) , \(\mathbf{u}+\mathbf{0}=\mathbf{u}, \quad \text { where } \quad \mathbf{0}=\langle 0,0\rangle\)
(d) \(\mathbf{u}+(-\mathbf{u})=\mathbf{0} \text {, where }-\langle a, b\rangle=\langle-a,-b\rangle\)
(e) \(a(\mathbf{u}+\mathbf{v})=a \mathbf{u}+a \mathbf{v}\)
(f) \((a+b) \mathbf{u}=a \mathbf{u}+b \mathbf{u}\)
(g) \((a b) \mathbf{u}=a(b \mathbf{u}) \)
(h) \(a \mathbf{0}=\mathbf{0}, 0 \mathbf{u}=\mathbf{0}\)
(i) \((1) \mathbf{u}=\mathbf{u},(-1) \mathbf{u}=-\mathbf{u}\)
(j) \(|a \mathbf{u}|=|a||\mathbf{u}|\)
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