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A force of $\sqrt{3} N$ makes equal angles with X-axis, Y-axis, and Z-axis. The possible value of force are

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$(\hat{i} + \hat{j} + \hat{k}) N$

$(- \hat{i} + \hat{j} - \hat{k}) N$

$(- \hat{i} - \hat{j} - \hat{k}) N$

$(- \hat{i} + \hat{j} + \hat{k}) N$

answer is A, C.

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Detailed Solution

$α = β = γ$

But ${cos}^{2} α + \cos^{2} β + \cos^{2} γ = 1$

$\Rightarrow 3 \cos^{2} α = 1 or cosα = \pm \frac{1}{\sqrt{3}}$

$∴ \vec{F} = Fcosα \hat{i} + Fcos β \hat{j} + Fcosγ \hat{k} \Rightarrow \pm (\hat{i} + \hat{j} + \hat{k}) N$

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