Question

The projection of the line segment joining the points $(1,-1,3)$ and $(2,-4,11)$ on the line joining the points $(-1,2,3)$ and $(3,-2,10)$ is

Answer 1

$\overrightarrow{AB}=\hat{i}-3\hat{j}+8\hat{k}$
$\overrightarrow{CD}=4\hat{i}-4\hat{j}+7\hat{k}$

Projection of $\overrightarrow{AB}$ on $\overrightarrow{CD}$ is,
$\frac{\overrightarrow{AB}\cdot \overrightarrow{CD}}{|\overrightarrow{CD}|}=\frac{4+12+56}{\sqrt{4^2+4^2+7^2}}=\frac{72}{9}=8$