A) \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
C) variable
D) None of these
Correct Answer: B
Solution :
Let the cube be of side\[a\]. Then, \[O(0,\,\,0,\,\,0),\,\,D(a,\,\,a,\,\,a),\,\,B(0,\,\,a,\,\,0)\]and\[G(a,\,\,0,\,\,a)\] Now, equations of diagonals \[OD\] 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 \[{{\cos }^{-1}}\left( \frac{{{a}^{2}}-{{a}^{2}}+{{a}^{2}}}{\sqrt{3{{a}^{2}}}\cdot \sqrt{3{{a}^{2}}}} \right)={{\cos }^{-1}}\left( \frac{1}{3} \right)\]You need to login to perform this action.
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