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(D) Let the direction ratios of the required line be $a, b, c$.Since the line is perpendicular to the lines with direction ratios $(1, 2, 3)$ and $(-3

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$\frac{x+1}{2} = \frac{y-3}{-7} = \frac{z+2}{4}$

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(D) Let the direction ratios of the required line be $a, b, c$.Since the line is perpendicular to the lines with direction ratios $(1, 2, 3)$ and $(-3, 2, 5)$,we have the following equations:$a + 2b + 3c = 0$ $(i)$$-3a + 2b + 5c = 0$ (ii)Using the cross-multiplication method to solve for $a, b, c$:$\frac{a}{(2)(5) - (3)(2)} = \frac{b}{(3)(-3) - (1)(5)} = \frac{c}{(1)(2) - (2)(-3)}$$\frac{a}{10 - 6} = \frac{b}{-9 - 5} = \frac{c}{2 + 6}$$\frac{a}{4} = \frac{b}{-14} = \frac{c}{8}$Dividing by $2$,we get the direction ratios as $(2, -7, 4)$.The equation of the line passing through $(-1, 3, -2)$ with direction ratios $(2, -7, 4)$ is:$\frac{x - (-1)}{2} = \frac{y - 3}{-7} = \frac{z - (-2)}{4}$$\frac{x+1}{2} = \frac{y-3}{-7} = \frac{z+2}{4}$

The equation of the line passing through the point $(-1, 3, -2)$ and perpendicular to each of the lines $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ and $\frac{x+2}{-3} = \frac{y-1}{2} = \frac{z+1}{5}$ is:

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