Question

Is the vector sum of the unit vectors $\overrightarrow{i}$ and $\overrightarrow{j}$ 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 $\overrightarrow{i}$ and $\overrightarrow{j}$ is not a unit vector, because the magnitude of the resultant of $\overrightarrow{i}$ and $\overrightarrow{j}$ is not one.

Magnitude of the resultant vector is given by
R = $\sqrt{1^2+1^2+\cos 90°}=\sqrt{2}$

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