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

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

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

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

answer is A, C.

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Detailed Solution

$∵ α = β = γ$

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

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

$∴ F = Fcos α \hat{i} + Fcos β \hat{j} + Fcos γ \hat{k}$

$Or F = \pm (\hat{i} + \hat{j} + \hat{k}) N$

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