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(A) The direction ratios of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$

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$6, 2, 3$

Vedclass · Answer

(A) The direction ratios of a line passing through two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.Given points are $(x_1, y_1, z_1) = (4, 3, -5)$ and $(x_2, y_2, z_2) = (-2, 1, -8)$.Direction ratios = $(-2 - 4, 1 - 3, -8 - (-5))$.Direction ratios = $(-6, -2, -3)$.Alternatively,taking the difference as $(x_1 - x_2, y_1 - y_2, z_1 - z_2)$ gives $(4 - (-2), 3 - 1, -5 - (-8)) = (6, 2, 3)$.Since the direction ratios are proportional,both $(-6, -2, -3)$ and $(6, 2, 3)$ represent the same line. Given the options,$(6, 2, 3)$ is the correct choice.

The direction ratios of the line joining the points $(4, 3, -5)$ and $(-2, 1, -8)$ are

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