Rewrite the equation of line $l$ in Cartesian form

Question

The question asks to rewrite the following vector equation of line $l$ in Cartesian form $$l: \vec{r}= (4\vec{i}+0\vec{j}+2\vec{k}) + \lambda(3\vec{i}+\vec{j}+0\vec{k})$$ When I try to do it I result in the following Cartesian equation $$\frac{x-4}{3}=y=\frac{z-2}{0}$$ Is this correct?

Answer 1

Notice that division by zero is not defined. So, you can write $$\frac{x-4}3=y,\quad z=2.$$