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

Draw the resultant direction of the two unit vectors hatiandhatj Use a

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