The direction cosines of the line joining the | vedclass

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Question

(A) Let the points be $P(4, 3, -5)$ and $Q(-2, 1, -8)$.The direction ratios $(a, b, c)$ of the line segment $PQ$ are given by $(x_2 - x_1, y_2 - y_1,

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$\left( \frac{6}{7}, \frac{2}{7}, \frac{3}{7} \right)$

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(A) Let the points be $P(4, 3, -5)$ and $Q(-2, 1, -8)$.The direction ratios $(a, b, c)$ of the line segment $PQ$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.$a = -2 - 4 = -6$$b = 1 - 3 = -2$$c = -8 - (-5) = -3$The distance $PQ = \sqrt{(-6)^2 + (-2)^2 + (-3)^2} = \sqrt{36 + 4 + 9} = \sqrt{49} = 7$.The direction cosines $(l, m, n)$ are given by $\left( \frac{a}{PQ}, \frac{b}{PQ}, \frac{c}{PQ} \right)$.$l = \frac{-6}{7}, m = \frac{-2}{7}, n = \frac{-3}{7}$.Alternatively,if we consider the direction from $Q$ to $P$,the direction cosines are $\left( \frac{6}{7}, \frac{2}{7}, \frac{3}{7} \right)$.Comparing with the given options,the correct option is $A$.

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

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