(D) Since $OA$ is equally inclined to the axes $OX, OY$ and $OZ$, the direction cosines are equal. Let the coordinates of $A$ be $(a, a, a)$.Given tha

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(D) Since $OA$ is equally inclined to the axes $OX, OY$ and $OZ$, the direction cosines are equal. Let the coordinates of $A$ be $(a, a, a)$.Given that the distance of $A$ from the origin $O(0,0,0)$ is $\sqrt{3}$ units.Therefore, $\sqrt{(a-0)^2 + (a-0)^2 + (a-0)^2} = \sqrt{3}$.$\sqrt{3a^2} = \sqrt{3}$.$|a|\sqrt{3} = \sqrt{3}$.$|a| = 1$, which implies $a = 1$ or $a = -1$.Thus, the coordinates of $A$ are $(1, 1, 1)$ or $(-1, -1, -1)$.Comparing this with the given options, the correct coordinate is $(1, 1, 1)$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

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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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A
$(3,3,3)$
B
$(-1,1,-1)$
C
$(-1,1,1)$
D
$(1,1,1)$

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Class 12

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THREE DIMENSIONAL GEOMETRY

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System of co-ordinates, Direction cosines and direction ratios, Projection

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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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