Find symmetric equations of the line containing the point $(1,-1,2)$ and in the direction of the vector $5\mathbf{i}-2\mathbf{j}+3\mathbf{k}$.

Solution The components of the vector $5\mathbf{i}-2\mathbf{j}+3 \mathbf{k}$ are all nonzero. So, we use $a=5$, $b=-2$, and $c=3$ and the coordinates of the point $(1,-1,2)$ to obtain the symmetric equations $$\frac{x-1}{5}=\frac{y+1}{-2}=\frac{z-2}{3}$$