Question

Is the vector sum of the unit vectors  \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

 

Answer 1

No, the vector sum of the unit vectors \[\vec{i}\] and  \[\vec{i}\]  is not a unit vector, because the magnitude of the resultant of \[\vec{i}\] and \[\vec{j}\] is not one.
Magnitude of the resultant vector is given by
R = \[\sqrt{1^2 + 1^2 + \cos90^\circ} = \sqrt{2}\]

Yes, we can multiply this resultant vector by a scalar number \[\frac{1}{\sqrt{2}}\] to get a unit vector.