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The angle between the lines xcos alpha1+...

The angle between the lines `xcos alpha_1+ysin alpha_1=p_1` and `xcos alpha_2+ysin alpha_2=p_2` is
(A)   `|alpha_1+alpha_2|`    (B)   `|alpha_1-alpha_2|`    (C)   `|2alpha_1|`    (D)   `|2alpha_2|`   

Text Solution

Verified by Experts

Equation of line 1, `L_1 =>xcos alpha_1+ysin alpha_1=p_1`
`=>y = -x(cos alpha_1)/(sin alpha_1) +p_1/sin alpha_1`
`=> y = -cot alpha_1 x +p_1/sin alpha_1`
Comparing it with, `y = mx+c`
Slope of `L_1(m_1) = -cotalpha_1`
Equation of line 1, `L_2 =>xcos alpha_2+ysin alpha_2=p_2`
`=>y = -x(cos alpha_2)/(sin alpha_2) +p_2/sin alpha_2`
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