The direction cosines of the line joining the | vedclass

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Question

(A) Let the points be $P = (-2, 4, -5)$ and $Q = (1, 2, 3)$.The direction ratios of the line segment $\overrightarrow{PQ}$ are given by $(x_2 - x_1, y

Vedclass · Accepted Answer

$\left(\frac{3}{\sqrt{77}}, \frac{-2}{\sqrt{77}}, \frac{8}{\sqrt{77}}\right)$

Vedclass · Answer

(A) Let the points be $P = (-2, 4, -5)$ and $Q = (1, 2, 3)$.The direction ratios of the line segment $\overrightarrow{PQ}$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1) = (1 - (-2), 2 - 4, 3 - (-5)) = (3, -2, 8)$.The magnitude of the vector $\overrightarrow{PQ}$ is $|\overrightarrow{PQ}| = \sqrt{3^2 + (-2)^2 + 8^2} = \sqrt{9 + 4 + 64} = \sqrt{77}$.The direction cosines $(l, m, n)$ are obtained by dividing the direction ratios by the magnitude:$l = \frac{3}{\sqrt{77}}$,$m = \frac{-2}{\sqrt{77}}$,$n = \frac{8}{\sqrt{77}}$.Thus,the direction cosines are $\left(\frac{3}{\sqrt{77}}, \frac{-2}{\sqrt{77}}, \frac{8}{\sqrt{77}}\right)$.

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

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