Three Dimensional Geometry Question 389
Question: Under what condition do $ \langle \frac{1}{\sqrt{2}},\frac{1}{2},k \rangle $ represent direction cosines of a line?
Options:
A) $ k=\frac{1}{2} $
B) $ k=-\frac{1}{2} $
C) $ k=\pm \frac{1}{2} $
D) K can take any value
Show Answer
Answer:
Correct Answer: C
Solution:
[c] For $ ( \frac{1}{\sqrt{2}},\frac{1}{2},k ) $ to represent direction cosines, we should have $ {{( \frac{1}{\sqrt{2}} )}^{2}}+{{( \frac{1}{2} )}^{2}}+k^{2}=1 $ or $ \frac{1}{2}+\frac{1}{4}+k^{2}=1\Rightarrow k=\pm \frac{1}{2} $
BETA
