Mathematics

Problem

Let

\mathbf{p}=4\mathbf{i}-\mathbf{j}+5\mathbf{k}

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

and

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

. Determine the vector

\mathbf{p}+2\mathbf{q}-\tfrac12\mathbf{r}