What angle does the vector xi + yj make with the horizontal ?

Vector xi + yj is the resultant of vector xi and yj. xi is 0° to the horizontal (the x axis), whereas yj is at 90° to the horizontal. That is, yj makes 90° with with the xi (which is on the horizontal). The resultant of two vectors cuts the angle between those vectors into two equal halves. Therefore, the vector xi + yj makes 45° with the horizontal.