The angle between the lines x cos alpha_1 + y | vedclass

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(B) The given lines are in the normal form $x \cos \alpha + y \sin \alpha = p$,where $\alpha$ is the angle that the normal to the line makes with the

Vedclass · Accepted Answer

$|\alpha_1 - \alpha_2|$

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(B) The given lines are in the normal form $x \cos \alpha + y \sin \alpha = p$,where $\alpha$ is the angle that the normal to the line makes with the positive $x$-axis.For the first line $x \cos \alpha_1 + y \sin \alpha_1 = p_1$,the normal makes an angle $\alpha_1$ with the $x$-axis.For the second line $x \cos \alpha_2 + y \sin \alpha_2 = p_2$,the normal makes an angle $\alpha_2$ with the $x$-axis.The angle between the two lines is equal to the angle between their normals.Therefore,the angle between the lines is $|\alpha_1 - \alpha_2|$.

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:

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