If vector a and vector b are two non zero vectors such thata bar +b bar =a bar -b bar/2 and a bar =2 b bar then the angle between a bar and b bar is:

Let the angle between the two vectors be x° a vector+b vector =a vector - b vector/2Therefore, by vector lawsa vector + b vector=√a×a + b×b + 2abcosx &a vector - b vector/2 = √ a×a +b/2×b/2-2ab/2cosxTherefore, Squaring both sides a×a + b×b + 2abcosx=a×a + b×b/4 - abcosx3/4b×b=abcosxb=4/3acosx Put b= 4/3acosxTherefore,3/4×16/9cosx × cos x =a×4/3a cos x4/3 a×a cos x × cos x =4/3a×a b cos xCos x = 1x=0°Therefore, the angle between the two vectors is 0°.