The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. What is the angle between A and B ?

The resultant of two vectors A and B is perpendicular to the vector A

1.	The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. What is the angle between A and B ?
Answer» Solution :Let, the unit vectors along `vecA, vecB and vecR " be"" " hata , HATB and hatc` respectively. Then `vecA=Ahata,vecB=Bhatb,vecR=Rhatc and Ahata+Bhatb=Rhatc` ` or, A(VEC(OP))/(OP)+B(vec(OQ))/(OS)=R(vec(OS))/(OS)` [Fig .2.62]. If `hatn` is the unit vector along theline CD, `vec(OP)xxhatn=OP SIN alphahatm=ONhatm,` `vec(OQ)xxhatn=ONhatm, vec(OS)xxhatn=ONhatm` where `hatm` is a unit vector perpendicular to the plane of THEVECTORS. Then , `A/(OP)vec(OP)xxhatn+B/(OQ)vec(OQ)xxhatn=R/(OS)vec(OS)xxhatn` `or, A/(OP) ONhatm+B/(OQ)hatm=R/(OS)ONhatm` `or, A/(OP)+B/(OQ)=R/(OS)`.