Mathematics

Problem

For the vectors

\mathbf{a}=2\hat{i}-\hat{j}+3\hat{k}

\mathbf{b}=-\hat{i}+4\hat{j}+2\hat{k}

and

\mathbf{c}=3\hat{i}+2\hat{j}-5\hat{k}

: (i) Calculate

(\mathbf{a}+\mathbf{b})+\mathbf{c}

. (ii) Calculate

\mathbf{a}+(\mathbf{b}+\mathbf{c})

. (iii) Verify that the two results are equal and comment on the property illustrated. (iv) Compute

\mathbf{a}+\mathbf{b}

and

\mathbf{b}+\mathbf{a}

separately. What property is demonstrated? c. (iii) Compare the answers obtained in (i) and (ii) and state the property verified. d. (iv) Compute

\mathbf{a}+\mathbf{b}

and

\mathbf{b}+\mathbf{a}

, then identify the property demonstrated.