The direction cosines of the line passing thr | vedclass

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(C) Let the points be $A(2, 3, -1)$ and $O(0, 0, 0)$.The direction ratios of the line $OA$ are $(2-0, 3-0, -1-0) = (2, 3, -1)$.The distance $OA$ is $\

Vedclass · Accepted Answer

$\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}$

Vedclass · Answer

(C) Let the points be $A(2, 3, -1)$ and $O(0, 0, 0)$.The direction ratios of the line $OA$ are $(2-0, 3-0, -1-0) = (2, 3, -1)$.The distance $OA$ is $\sqrt{2^2 + 3^2 + (-1)^2} = \sqrt{4 + 9 + 1} = \sqrt{14}$.The direction cosines $(l, m, n)$ are given by $\frac{a}{r}, \frac{b}{r}, \frac{c}{r}$, where $(a, b, c)$ are direction ratios and $r$ is the distance.Thus, $l = \frac{2}{\sqrt{14}}, m = \frac{3}{\sqrt{14}}, n = \frac{-1}{\sqrt{14}}$.Alternatively, for the line $AO$, the direction ratios are $(0-2, 0-3, 0-(-1)) = (-2, -3, 1)$.The direction cosines are $\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}$.Comparing with the options, option $C$ is correct.

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

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