question_answer

If in the given figure \[\overrightarrow{OA}=\mathbf{a},\,\,\,\overrightarrow{OB}=\mathbf{b}\] and \[AP\,\,:\,\,PB=m\,\,:\,\,n,\] then \[\overrightarrow{OP}=\]                                    [RPET 1981; MP PET 1988]

A) \[\frac{m\,\mathbf{a}+n\,\mathbf{b}}{m+n}\]               

B) \[\frac{n\,\mathbf{a}+m\,\mathbf{b}}{m+n}\]

C) \[m\,\mathbf{a}-n\,\mathbf{b}\]         

D) \[\frac{m\,\mathbf{a}-n\,\mathbf{b}}{m-n}\]