Three Dimensional Geometry Question 213
Question: The angle between the lines whose direction cosines are proportional to (1, 2, 1) and (2, ?3, 6) is
Options:
A) $ {{\cos }^{-1}}( \frac{2}{7\sqrt{6}} ) $
B) $ {{\cos }^{-1}}( \frac{1}{7\sqrt{6}} ) $
C) $ {{\cos }^{-1}}( \frac{3}{7\sqrt{6}} ) $
D) $ {{\cos }^{-1}}( \frac{5}{7\sqrt{6}} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \theta ={{\cos }^{-1}}[ \frac{(1)(2)+(2)(-3)+(1)(6)}{\sqrt{1^{2}+2^{2}+1^{2}}\sqrt{2^{2}+{{(-3)}^{2}}+6^{2}}} ] $ $ {{\cos }^{-1}},[ \frac{2-6+6}{\sqrt{6}\sqrt{49}} ]={{\cos }^{-1}}[ \frac{2}{7\sqrt{6}} ] $ .
BETA
