$\begin{aligned} & \mathrm{A}=(-2,2,3) ; \mathrm{B}=(3,2,2) ; \mathrm{C}=(4,-3,5) \text { and } \mathrm{D}=(7,-5,-1) \\ & \overline{\mathrm{AB}}=5 \hat{\mathrm{i}}-\hat{\mathrm{k}} \text { and } \overline{\mathrm{CD}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-6 \hat{\mathrm{k}} \\ & \text { Projection of } \overline{\mathrm{AB}} \text { on } \overline{\mathrm{CD}} \\ & =\frac{\overline{\mathrm{AB}} \cdot \overline{\mathrm{CD}}}{|\mathrm{CD}|}=\frac{(5 \hat{\mathrm{i}}-\hat{\mathrm{k}}) \cdot(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-6 \hat{\mathrm{k}})}{\sqrt{(3)^2+(-2)^2+(-6)^2}}=\frac{15+6}{7}=3\end{aligned}$