Question

The projection of point $P(\vec{p})$ on the plane $\vec{r}â‹\dots \vec{n}=q$ is $(\vec{s})$, then

• A. $\vec{s}=\frac{(q−\vec{p}â‹\dots \vec{n})\vec{n}}{âˆ\pounds \vec{n}{âˆ\pounds }^2}$
• B. $\vec{s}=\vec{p}+\frac{(q−\vec{p}â‹\dots \vec{n})\vec{n}}{âˆ\pounds \vec{n}{âˆ\pounds }^2}$
• C. $\vec{s}=\vec{p}−\frac{(\vec{p}â‹\dots \vec{n}â‹\dots )\vec{n}}{âˆ\pounds \vec{n}{âˆ\pounds }^2}$
• D. $\vec{s}=\vec{p}−\frac{(q−\vec{p}â‹\dots \vec{n})\vec{n}}{âˆ\pounds \vec{n}{âˆ\pounds }^2}$

Answer 1

Answer: (B)

We have $\vec{s}−\vec{p}=λ\vec{n}$
and $\vec{s}â‹\dots \vec{n}=q$. Thus,
$(λ\vec{n}+\vec{p})â‹\dots \vec{n}=q$
or$λ=\frac{\overrightarrow{q−p}â‹\dots \vec{n}}{âˆ\pounds \vec{n}{âˆ\pounds }^2}$
$⇒\vec{s}=\vec{p}+\frac{(q−\vec{p}â‹\dots \vec{n})\vec{n}}{{\vec{n}âˆ\pounds }^2}$