Match List-I with List-II

List-I	List-II
(A) Equations of line through $(5, -4, 6)$ with direction ratios $3, 7, 2$	(I) $\frac{x+3}{5} = \frac{y+7}{-4} = \frac{z+2}{6}$
(B) Equations of line through $(3, 7, 2)$ with direction ratios $5, -4, 6$	(II) $\frac{x-3}{5} = \frac{y-7}{-4} = \frac{z-2}{6}$
(C) Equations of line through $(-5, 4, -6)$ with direction ratios $3, 7, 2$	(III) $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$
(D) Equations of line through $(-3, -7, -2)$ with direction ratios $5, -4, 6$	(IV) $\frac{x+5}{3} = \frac{y-4}{7} = \frac{z+6}{2}$

Choose the correct answer from the options given below:

The equation of a line passing through a point $(x_1, y_1, z_1)$ with direction ratios $a, b, c$ is given by:

$\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$

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For line through $(5, -4, 6)$ with direction ratios $3, 7, 2$:

$x_1 = 5$, $y_1 = -4$, $z_1 = 6$

$a = 3$, $b = 7$, $c = 2$

$\frac{x - 5}{3} = \frac{y - (-4)}{7} = \frac{z - 6}{2}$

$\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2}$

This matches (III)

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For line through $(3, 7, 2)$ with direction ratios $5, -4, 6$:

$x_1 = 3$, $y_1 = 7$, $z_1 = 2$

$a = 5$, $b = -4$, $c = 6$

$\frac{x - 3}{5} = \frac{y - 7}{-4} = \frac{z - 2}{6}$

This matches (II)

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For line through $(-5, 4, -6)$ with direction ratios $3, 7, 2$:

$x_1 = -5$, $y_1 = 4$, $z_1 = -6$

$a = 3$, $b = 7$, $c = 2$

$\frac{x - (-5)}{3} = \frac{y - 4}{7} = \frac{z - (-6)}{2}$

$\frac{x + 5}{3} = \frac{y - 4}{7} = \frac{z + 6}{2}$

This matches (IV)

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For line through $(-3, -7, -2)$ with direction ratios $5, -4, 6$:

$x_1 = -3$, $y_1 = -7$, $z_1 = -2$

$a = 5$, $b = -4$, $c = 6$

$\frac{x - (-3)}{5} = \frac{y - (-7)}{-4} = \frac{z - (-2)}{6}$

$\frac{x + 3}{5} = \frac{y + 7}{-4} = \frac{z + 2}{6}$

This matches (I)

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Therefore, the correct matching is:

(A) → (III), (B) → (II), (C) → (IV), (D) → (I)