Three Dimensional Geometry Question 181
Question: The angle between two diagonals of a cube will be
[MP PET 1996, 2000; RPET 2000, 02; UPSEAT 2004]
Options:
A) $ {{\sin }^{-1}}1/3 $
B) $ {{\cos }^{-1}}1/3 $
C) Variable
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let the cube be of side ‘a’
$ O,(0,0,0),D,(a,a,a),B,(0,a,0),G,(a,0,a) $
Then equation of OD and BG are $ \frac{x}{a}=\frac{y}{a}=\frac{z}{a} $ and $ \frac{x}{a}=\frac{y-a}{-a}=\frac{z}{a} $ respectively.
Hence, angle between OD and BG is
$ {{\cos }^{-1}}( \frac{a^{2}-a^{2}+a^{2}}{\sqrt{3a^{2}}.,\sqrt{3a^{2}}} )={{\cos }^{-1}},( \frac{1}{3} ) $ . Note: Students should remember this question as a fact.
BETA
