The magnitude of resultant of three unit vectors cannot be

Given that

Three unit vectors.

Let us try the possible resultant of the given three unit vectors.

(i) They can form an equilateral triangle

So

Then we will get resultant = zero will have magnitude.

(ii) They can present in the same direction along the straight line

Then resultant will have magnitude = 3 units.

(iii) We can frame them along same line

Such that two of them in same direction and third one in opposite

direction.

Then resultant will have magnitude = 1.

We can observe that the magnitude of resultant of three unit vector will lie between 0 (minimum) and 3 (maximum)

So it cannot take the value $\text{3}\sqrt{2}$