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