Three-Dimensional-Geometry Question 442
Question: The number of straight lines that are equally inclined to the three dimensional co-ordinate axes, is
[MP PET 1994]
Options:
A) 2
B) 4
C) 6
D) 8
Show Answer
Answer:
Correct Answer: B
Solution:
Since $ \alpha =\beta =\gamma ,\Rightarrow {{\cos }^{2}}\alpha +{{\cos }^{2}}\alpha +{{\cos }^{2}}\alpha =1 $
$ \Rightarrow \alpha ={{\cos }^{-1}}( \pm ,\frac{1}{\sqrt{3}} ) $ So, there are four lines whose direction cosines are $ ( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} ),,( \frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} ),,( \frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}} ), $ $ ( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}} ) $ .
BETA
