Three Dimensional Geometry Question 378
Question: The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is
[MP PET 1995; RPET 2001]
Options:
A) 12
B) 50
C) $ 5\sqrt{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let the line segment be AB, then as given
$ AB\cos \alpha =3 $ , $ AB\cos \beta =4, $ , $ AB\cos \gamma =5 $
$ ,\Rightarrow AB^{2}({{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma ) $ $ =3^{2}+4^{2}+5^{2} $
$ AB=\sqrt{9+16+25}=5\sqrt{2} $ ,
where $ \alpha ,\beta $ and $ \gamma $ are the angles made by the line with the axes.
BETA
