The set of values of alpha for which the angl | vedclass

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(B) Given lines are $L_1: (\alpha + 1)x + 2y + 5 = 0$ and $L_2: 4x + \alpha y - 3 = 0$.To make the constant terms positive,rewrite $L_2$ as $-4x - \al

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$\left( -\frac{2}{3}, \infty \right)$

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(B) Given lines are $L_1: (\alpha + 1)x + 2y + 5 = 0$ and $L_2: 4x + \alpha y - 3 = 0$.To make the constant terms positive,rewrite $L_2$ as $-4x - \alpha y + 3 = 0$.Let $A_1 = \alpha + 1, B_1 = 2, C_1 = 5$ and $A_2 = -4, B_2 = -\alpha, C_2 = 3$.The angle bisector containing the origin is given by $\frac{A_1x + B_1y + C_1}{\sqrt{A_1^2 + B_1^2}} = \frac{A_2x + B_2y + C_2}{\sqrt{A_2^2 + B_2^2}}$.For the bisector to be the obtuse angle bisector,we check the sign of $A_1A_2 + B_1B_2$.$A_1A_2 + B_1B_2 = (\alpha + 1)(-4) + (2)(-\alpha) = -4\alpha - 4 - 2\alpha = -6\alpha - 4$.For the origin-containing bisector to be the obtuse one,we require $A_1A_2 + B_1B_2 $-6\alpha - 4  -\frac{2}{3}$.

The set of values of $\alpha$ for which the angle bisector of the lines $(\alpha + 1)x + 2y + 5 = 0$ and $4x + \alpha y - 3 = 0$ containing the origin is also the obtuse angle bisector,is:

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