Given that, |b|=2|a| .......(1) and angle between a and b=120° Now we have, a.b=|a||b|cos120° From (1) we have a.b=|a|(2a|)(−
1
2
) a.b=−|a|2 ......(2) Since (a+xb) and (a−b) are at right angle (a+xb).(a−b)=0 |a|2−a.b+xa.b−x|b|2=0 |a|2+a.b(x−1)−x|b|2=0 From (1) & (2), we have |a|2−(x−1)|a|2−4x|a|2=0 |a|2×[1−x+1−4x]=0 |a|2[2−5x]=0 |a|2≠0.so,2−5x=0 x=