If the points \(P, Q\) and \(R\) are with the position vectors \(\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}\) and \(-8 \hat{i}+13 \hat{j}\) respectively, then these points are

\(\begin{aligned}
\overline{P Q} & =-2 \hat{i}+3 \hat{j}+2 \hat{k}-(\hat{i}-2 \hat{j}+3 \hat{k}) \\
& =-3 \hat{i}+5 \hat{j}-\hat{k} \\
\overline{Q R} & =-8 \hat{i}+13 \hat{j}-(-2 \hat{i}+3 \hat{j}+2 \hat{k}) \\
& =-6 \hat{i}+10 \hat{j}-2 \hat{k} \\
& =2(-3 \hat{i}+5 \hat{j}-\hat{k})=2 \overline{P Q}
\end{aligned}\)
\(\therefore \quad \overline{\mathrm{QR}}\) is a scalar multiple of \(\overline{\mathrm{PQ}}\).
\(\therefore \quad \overline{\mathrm{QR}}\) and \(\overline{\mathrm{PQ}}\) are parallel to each other with point Q in common.
\(\therefore \quad\) Points \(\mathrm{P}, \mathrm{Q}\) and R are collinear and Q lies between P and R .