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(C) The equation of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $\frac{x-x_1}{x_2-x_1} = \frac{y-y_1}{y_2-y_

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$x = 3 - 2\lambda, y = 4 - 5\lambda, z = -7 + 13\lambda$

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(C) The equation of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $\frac{x-x_1}{x_2-x_1} = \frac{y-y_1}{y_2-y_1} = \frac{z-z_1}{z_2-z_1} = \lambda$. Substituting the given points $A(3, 4, -7)$ and $B(1, -1, 6)$: $\frac{x-3}{1-3} = \frac{y-4}{-1-4} = \frac{z-(-7)}{6-(-7)} = \lambda$ $\frac{x-3}{-2} = \frac{y-4}{-5} = \frac{z+7}{13} = \lambda$ From this,we get the parametric equations: $x - 3 = -2\lambda \implies x = 3 - 2\lambda$ $y - 4 = -5\lambda \implies y = 4 - 5\lambda$ $z + 7 = 13\lambda \implies z = -7 + 13\lambda$ Thus,the correct option is $C$.

The parametric equations of a line passing through the points $A(3, 4, -7)$ and $B(1, -1, 6)$ are

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