Fined the unit vector in the direction of vector ` vec P Q` , where `P` and `Q` are the points (1,2,3) and (4,5,6), respectively.

Explanation

\begin{aligned}
\vec{P}=\hat{i}+2 \hat{j}+3 \hat{k} \quad \vec{Q}=4 \hat{i}+5 \hat{j}+6 \hat{k}\\
\overrightarrow{P Q}=\vec{Q}-\vec{P}=4 \hat{i}+5 \hat{j}+6 \hat{k}-\hat{i}-2 \hat{j}-3 \hat{k}\\
\overrightarrow{P Q}=3 \hat{i}+3 \hat{j}+3 \hat{k}=3(\hat{i}+\hat{j}+\hat{k})=\overrightarrow{P Q}\\
\hat{P Q}=\frac{\overrightarrow{P Q}}{|\overrightarrow{P Q}|} \quad|\overrightarrow{P Q}|=\sqrt{3^{2}(1+1+1)}=3 \sqrt{3}\\
\text { Unit vector }=\frac{1}{3 \sqrt{3}}[3(\hat{i}+\hat{j}+\hat{k})]=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})
\end{aligned}