Question

A and B are two unit vectors and theta is the angle between them then a + b is a unit vector if

Answer 1

The magnitude of vector addition is given as underroot A2+ B2+2ABcosΦ
Given a & b are unit vectors, we have the magnitude as underroot 1^2 + 1^2 + 2(1)(1)cos90 degree = underroot 2
Using tangent function, Perpendicular/ Base = 1/1 = tan 45 degree
Thus, a+b is not a unit vector but has a magnitude of underroot 2 at an angle of 45 degrees from x axis.