The cosine of the angle between vectors p and q such that 2p+q=i+j , p+2q=i-j is Share with your friends Share 2 Sandeep Saurav answered this Dear Student, Given : 2 p ⇀+ q ⇀= i^ + j^ and p ⇀+2 q ⇀= i^ - j^ To calculate : cosine of angle between p ⇀and q ⇀.solution : 2 p ⇀+ q ⇀= i^ + j^ ..................................1 p ⇀+2 q ⇀= i^ - j^ ..................................2Multiplying 2 with 2 subtract from 1⇒(2 p ⇀+ q ⇀)-2( p ⇀+2 q ⇀)=(i^ + j^)-2( i^ - j^)⇒2 p ⇀-2 p ⇀+ q ⇀-4 q ⇀= i^ - 2 i^ + j^+2 j^⇒-3 q ⇀=- i^+3 j^⇒ q ⇀=-1-3 i^+3-3 j^⇒ q ⇀=13 i^- j^......................................3putting the value of 3 into 2 p ⇀+2 q ⇀= i^ - j^⇒ p ⇀+2(13 i^- j^)= i^ - j^⇒ p ⇀+23 i^-2 j^= i^ - j^⇒ p ⇀=-23 i^+2 j^+ i^ - j^⇒ p ⇀=13 i^+ j^.......................................4taking dot product of 3 and 4⇒ p ⇀. q ⇀=| p ⇀| | q ⇀| cos θ⇒cos θ= p ⇀. q ⇀| p ⇀| | q ⇀|⇒cos θ=(13 i^+ j^).(13 i^- j^)((13)2+12) ((13)2+12)⇒cos θ=(13)2 -1((13)2+12)2⇒cos θ=-89109⇒cos θ=-45 Hope this information will clear your doubts about topic. If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible. Keep posting!! Regards 2 View Full Answer