Given that,

Magnitude of = 2√3

Also, given that

Vector is equally inclined to the three axes.

This means, direction cosines of the unit vector will be same. The direction cosines are (l, m, n).

⇒ l = m = n

The direction cosines of a vector are simply the cosines of the angles between the vector and the three coordinate axes.

We know the relationship between direction cosines is,

l² + m² + n² = 1

⇒ l² + l² + l² = 1 [∵ l = m = n]

⇒ 3.l² = 1

Also, we know that is represented in terms of direction cosines as,

We are familiar with the formula,

To find ,

Substituting values of and .

Thus, the value of is .