Is the vector sum of the unit vectors and a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

If we take the vector sum of unit vectors and , as per the vector law of addition the resultant vector magnitude is not unit, but it is . The angle between and is 90° , thus we have . This sum can be multiplied by a scalar in order to get a unit vector, by multiplying the resultant with we can get a unit vector. Thus, we have