the resultant of two vectors P and Q is perpendicular to P and its magnitude is half of that of Q. Whats the angle between P and Q?

Res = P + Q. [given]Res is perpendicular to P. [given]|res| = 1/2*Q. [given]Res^ = P^ +Q^ + 2*PQ cos € {here € = angle}Cos € = - P/Q. [formula].Res^ = P^ +Q^ + 2*PQ (- P/Q). Res^ = P^ +Q^ - 2P^Q/Q. Res^ = P^ +Q^ -2P^. Res^ = Q^ - P^. (1/2*Q)^ = Q^ - P^. Q^/4 =Q^ - P^. P^ = Q^ -Q^/4. P^ = 3Q^/4. P^ = 3/4 Q. Cos € = - P/Q. Cos € = -underoot 3/ 2. Cos €= - cos 30 = cos (180-30). = cos 150€ = 150 (ans).

Take P and Q instead of A and B respectively.

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