Draw the resultant direction of the two unit vectors `hatiandhatj` Use a 2-dimensional Cartesian ystem. Is `hati+hatj` a unit vector?

Explanation

By using the triangular law of addition `hati+hatj` as shown in the following figure,

The definition of unit vector is `hatA.hatA=1`
But here, `(hati+hatj).(hati+hatj)=hati.hati+hati.hatj+hatj.hati+hatj.hatj=1+0+0+1=2` SO, `hati+hatj` is not a unit vector.
To make any vector to a unit vector, must divide the vector by its magnitude, `hatA=(hatA)/(|vecA|)`
The magnitude of the vector `hati+hatj=sqrt2`
Hence, the unit vector is `(hati+hatj)/(sqrt2)`.