The projection of the segment joining (1,-1,3) and (2,-4,11) on the line joining (-1,2,3) …

Question

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

Answer: 8

Accepted Answer

$\vec{PQ}=(1,-3,8)$, $\vec{RS}=(4,-4,7)$, $|\vec{RS}|=\sqrt{16+16+49}=9$.

$$\text{Projection} = \frac{\vec{PQ}\cdot\vec{RS}}{|\vec{RS}|} = \frac{4+12+56}9 = \frac{72}9=8$$

Solutions · 1