Let P be a plane passing through the points (2,1,0), (4,1,1) and (5,0,1) and R be any poin…

Question

Let $P$ be a plane passing through the points $(2,1,0)$, $(4,1,1)$ and $(5,0,1)$ and $R$ be any point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:

Accepted Answer

Plane passing through  (2, 1, 0), (4, 1, 1) and
(5, 0, 1) is

$$\left| {\begin{pmatrix} {x - 2} & {y - 1} & {z - 0}  \
   {4 - 2} & {1 - 1} & {1 - 0}  \
   {5 - 2} & {0 - 1} & {1 - 0}  \

\end{pmatrix} } \right|$$ = 0

$$ \Rightarrow $$  x + y -- 2z = 3

$$ \therefore $$  Image of R(2, 1, 6) in this plane is

$${{x - 2} \over 1} = {{y - 1} \over 1} = {{z - 6} \over { - 2}} =  - 2{{\left( {2 + 1 - 12 - 3} \right)} \over {1 + 1 + 4}}$$

$$ \therefore $$ (x, y, z) = (6, 5, --2)

Solutions · 1