A) \[\frac{1}{3}\]
B) \[\frac{1}{2}\]
C) \[\frac{2}{3}\]
D) \[\frac{1}{\sqrt{3}}\]
Correct Answer: A
Solution :
Let every side of a cube is a and O, A, G, D are its vertex \[\therefore \]Direction cosines of OG and AD are \[\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\]and\[\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\] Cosine of the angle between OG and AD ie, \[\cos \theta =ll'+mm'+nn'\] \[=\frac{1}{3}+\frac{1}{3}-\frac{1}{3}=\frac{1}{3}\]You need to login to perform this action.
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