THE resultant of vector a AND b is perpendicular to the vector a And its magnitude is half that of vector b . find the angle between vector a And b ?

Question

michele_laino · Answer

please what operation do you mean when you write "a AND b"?

abhisindhu · Answer

I WROTE a in small so that there wouldn't be any confusion . YOU can take vectors AS P AND Q too

michele_laino · Answer

please wait, I think that the expression "a AND b" means vector addition, so the problem is solved by these equations:
$$\begin{gathered}
  {\left( {\frac{b}{2}} \right)^2} = {a^2} + {b^2} - 2ab\cos \theta ,\quad \left( {{\text{Theorem of Carnot}}} \right) \hfill \
   \hfill \
  {b^2} = {a^2} + {\left( {\frac{b}{2}} \right)^2},\quad \left( {{\text{Theorem of Pitagora}}} \right) \hfill \ 
\end{gathered} $$

abhisindhu · Answer

CAN you help me by illustrating it in a much better way 
thanks

michele_laino · Answer

here is the situation:
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