A) \[({{\alpha }_{1}}+{{\alpha }_{2}})\]
B) \[({{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}})\]
C) \[2{{\alpha }_{1}}\]
D) \[2{{\alpha }_{2}}\]
Correct Answer: B
Solution :
\[\theta ={{\tan }^{-1}}\left[ \frac{-\cot {{\alpha }_{1}}+\cot {{\alpha }_{2}}}{1+\cot {{\alpha }_{1}}\cot {{\alpha }_{2}}} \right]\] \[={{\tan }^{-1}}\left[ \frac{\tan {{\alpha }_{2}}-\tan {{\alpha }_{1}}}{1+\tan {{\alpha }_{2}}\tan {{\alpha }_{1}}} \right]=({{\alpha }_{2}}\tilde{\ }{{\alpha }_{1}})\] Aliter: Obviously, first line makes angle \[\frac{\pi }{2}+{{\alpha }_{1}}\]with the x-axis and second line makes the angle \[\frac{\pi }{2}+{{\alpha }_{2}}\]. Therefore, angle between these two lines is \[{{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}}\].
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