Question: The angle between the lines $ x\cos {\alpha_1}+y\sin {\alpha_1}=p_1 $ and $ x\cos {\alpha_2}+y\sin {\alpha_2}=p_2 $ is
Options:
A) $ ({\alpha_1}+{\alpha_2}) $
B) $ ({\alpha_1}\tilde{\ }{\alpha_2}) $
C) $ 2{\alpha_1} $
D) $ 2{\alpha_2} $
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Answer:
Correct Answer: B
Solution:
- $ \theta ={{\tan }^{-1}}[ \frac{-\cot {\alpha_1}+\cot {\alpha_2}}{1+\cot {\alpha_1}\cot {\alpha_2}} ] $ $ ={{\tan }^{-1}}[ \frac{\tan {\alpha_2}-\tan {\alpha_1}}{1+\tan {\alpha_2}\tan {\alpha_1}} ]=({\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} $ .
BETA
