A vector $e$ whose magnitude is 10 and d.c's are all equal angles made by $e$ with coordinate axis are less than $90^{0}$ is

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$\frac{1}{\sqrt{3}} (i + j + k)$

$\frac{10}{\sqrt{3}} (i + j + k)$

$\frac{10}{\sqrt{3}} (i - j + k)$

$\frac{10}{\sqrt{3}} (i - j - k)$

answer is B.

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Detailed Solution

$α = β = γ \Rightarrow \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \Rightarrow \cos^{2} α = \frac{1}{3} \Rightarrow cosα = \frac{1}{3} |e| = 10 \Rightarrow e = \frac{10}{\sqrt{3}} (i + j + k)$

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