Let OA = a , OB = b and if the vector along the angle bisector of AOB is given by x a | a | + y b | b | then

Step-by-step solution

Let a and b represent the vectors OA and OB respectively. The angle bisector direction is given by the sum of the unit vectors: a | a | + b | b | . Comparing with the given expression x a | a | + y b | b | , the coefficients must be equal since the unit vectors are linearly independent. Therefore x = y , or equivalently x - y = 0 . x - y = 0 The correct option is A .