JEE Main & Advanced
Mathematics
Three Dimensional Geometry
Question Bank
Critical Thinking
question_answer
If \[P\equiv (0,\,1,\,0),Q\equiv (0,\,0,\,1)\], then projection of \[PQ\] on the plane \[x+y+z=3\]is [EAMCET 2002]
A)\[\sqrt{3}\]
B)3
C)\[\sqrt{2}\]
D)2
Correct Answer:
C
Solution :
Given plane is \[x+y+z-3=0\]. From point P and Q draw PM and QN perpendicular on the given plane and QR ^ MP. \[|MP|\,=\frac{0+1+0-3}{\sqrt{{{1}^{2}}+{{1}^{2}}+{{1}^{2}}}}=\frac{-2}{\sqrt{3}}\], \[|NQ|\,=\frac{-2}{\sqrt{3}}\]