Comment
Share
Q)

# If $P(0,1,0)\:and\:Q(0,0,1)$ are two points in space, then the projection of $PQ$ on the plane $x+y+z=3$ is ?

$\begin{array}{1 1} (a)\:\:2\:\:\:\qquad\:\:\\ (b)\:\:3\:\:\:\\ (c)\:\:\sqrt 2\:\:\: \\ (d)\:\:\sqrt 3. \end{array}$

Comment
A)
• Projection of a line segment $PQ$ on any plane is $PQ\:cos\theta$ where $\theta$ is angle between the line $PQ$ and the plane.
Given $P(0,1,0)\:and\:Q(0,0,1)$.
$\therefore PQ=\sqrt$
Given equation of the plane is $x+y+z=3$
Normal to the plane is $\overrightarrow n=(1,1,1)$
Angle $\theta$ between the line $\overrightarrow {PQ}$ and the plane is given by
$sin\theta=\large\frac{\overrightarrow {PQ}.\overrightarrow n}{|\overrightarrow {PQ}||\overrightarrow b|}=\large\frac{(0,-1,1).(1,1,1)}{\sqrt 2. \sqrt 3}$$=0$
$\Rightarrow\:\theta=0$
Projection of $PQ$ on the plane is $PQ\:cos\theta=PQ=\sqrt 2$