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+1 vote
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Write a unit vector making equal acute angles with a coordinates axes.

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Let the angle made be α. We know that the sum of squares of direction cosines of a vector is 1. SO, we get

cos2α+cos2α+cos2α = 1

Since, α is acute therefore \(cos\,\alpha= \cfrac{1}{\sqrt3}\)

Any vector, if it’s magnitude and direction cosines are given can be written as 

So the required vector is

Rationalizing, we get

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