If OA is equally inclined to OX, OY and OZ an | vedclass

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(D) Let the coordinates of point $A$ be $(x, y, z)$.Since $OA$ is equally inclined to the axes $OX, OY$ and $OZ$,the direction cosines $l, m, n$ are e

Vedclass · Accepted Answer

$(1,1,1)$

Vedclass · Answer

(D) Let the coordinates of point $A$ be $(x, y, z)$.Since $OA$ is equally inclined to the axes $OX, OY$ and $OZ$,the direction cosines $l, m, n$ are equal.Thus,$l = m = n$.Since $l^2 + m^2 + n^2 = 1$,we have $3l^2 = 1$,which implies $l = m = n = \pm \frac{1}{\sqrt{3}}$.The coordinates of $A$ are given by $(r l, r m, r n)$,where $r$ is the distance from the origin.Given $r = \sqrt{3}$,the coordinates are $(\sqrt{3} 	imes \pm \frac{1}{\sqrt{3}}, \sqrt{3} 	imes \pm \frac{1}{\sqrt{3}}, \sqrt{3} 	imes \pm \frac{1}{\sqrt{3}})$.This simplifies to $(1, 1, 1)$ or $(-1, -1, -1)$.Comparing with the given options,the correct coordinate is $(1, 1, 1)$.

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin,then $A$ is:

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