If $4\hat{i}+\hat{j}-3\hat{k}$ and $p\hat{i}+q\hat{j}-2\hat{k}$ are collinear vectors, then what are the possible values of $p$ and $q$ respectively?

Two vectors $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$ and $\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ are collinear if their components are proportional:
$$\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}=\lambda$$
Given vectors: $4\hat{i}+1\hat{j}-3\hat{k}$ and $p\hat{i}+q\hat{j}-2\hat{k}$ $
$\frac{4}{p}=\frac{1}{q}=\frac{-3}{-2}$ $
$$\frac{4}{p}=\frac{1}{q}=\frac{3}{2}$$
Equating the first and third parts:
$$\frac{4}{p}=\frac{3}{2}⟹3p=8⟹p=\frac{8}{3}$$
Equating the second and third parts:
$$\frac{1}{q}=\frac{3}{2}⟹3q=2⟹q=\frac{2}{3}$$
So, $p=\frac{8}{3}$ and $q=\frac{2}{3}$.