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If $O A$ is equally inclined to $O X, O Y$ and $O Z$ and if $A$ is $\sqrt{3}$ units from the origin, then $A$ is :
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The correct answer is:
$(1,1,1)$
Since $O A$ is equally inclined to $O X, O Y$ and $O Z$. $\therefore$ Co-ordinates of $A$ are $(a, a, a)$. Also $O A=\sqrt{3}$
$\therefore \quad \sqrt{(a-0)^2+(a-0)^2+(a-0)^2}=\sqrt{3}$
$\Rightarrow \quad \sqrt{3 a^2}=\sqrt{3}$
$\Rightarrow \quad a^2=1$
$\Rightarrow \quad a= \pm 1$
$\therefore$ Co-ordinates of $A$ are $(1,1,1)$ or $(-1,-1,-1)$.
$\therefore \quad \sqrt{(a-0)^2+(a-0)^2+(a-0)^2}=\sqrt{3}$
$\Rightarrow \quad \sqrt{3 a^2}=\sqrt{3}$
$\Rightarrow \quad a^2=1$
$\Rightarrow \quad a= \pm 1$
$\therefore$ Co-ordinates of $A$ are $(1,1,1)$ or $(-1,-1,-1)$.
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