logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  3-D Geometry
0 votes

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} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • 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 $P(0,1,0)\:and\:Q(0,0,1)$.
$\therefore PQ=\sqrt$
<< Enter Text >>
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$
$\Rightarrow\:\theta=0$
Now
Projection of $PQ$ on the plane is $PQ\:cos\theta=PQ=\sqrt 2$
answered Jan 6, 2014 by rvidyagovindarajan_1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...