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(D) The equation of the plane bisecting the angle between the planes $P_1: 2x - y + 2z + 3 = 0$ and $P_2: 3x - 2y + 6z + 8 = 0$ is given by the formul

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$23x - 13y + 32z + 45 = 0$

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(D) The equation of the plane bisecting the angle between the planes $P_1: 2x - y + 2z + 3 = 0$ and $P_2: 3x - 2y + 6z + 8 = 0$ is given by the formula:$\frac{2x - y + 2z + 3}{\sqrt{2^2 + (-1)^2 + 2^2}} = \pm \frac{3x - 2y + 6z + 8}{\sqrt{3^2 + (-2)^2 + 6^2}}$Calculating the denominators:$\sqrt{4 + 1 + 4} = \sqrt{9} = 3$$\sqrt{9 + 4 + 36} = \sqrt{49} = 7$So,the equation becomes:$\frac{2x - y + 2z + 3}{3} = \pm \frac{3x - 2y + 6z + 8}{7}$Cross-multiplying:$7(2x - y + 2z + 3) = \pm 3(3x - 2y + 6z + 8)$Case $1$ (Positive sign):$14x - 7y + 14z + 21 = 9x - 6y + 18z + 24$$5x - y - 4z - 3 = 0$Case $2$ (Negative sign):$14x - 7y + 14z + 21 = -(9x - 6y + 18z + 24)$$14x - 7y + 14z + 21 = -9x + 6y - 18z - 24$$23x - 13y + 32z + 45 = 0$Comparing with the given options,the correct equation is $23x - 13y + 32z + 45 = 0$.

Find the equation of the plane bisecting the angle between the planes $2x - y + 2z + 3 = 0$ and $3x - 2y + 6z + 8 = 0$.

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