cho ΔABC ,M,N,P thỏa mãn : vecto MB = -1/3 vecto MC,vecto NC = 3/2 vecto NA, vecto PA = -2 vecto PB, C/M:M,N,P thẳng hàng

$$\eqalign{ & \overrightarrow {NP} = \overrightarrow {NA} + \overrightarrow {AP} \cr & \,\,\,\,\,\,\,\, = 2\overrightarrow {AC} + {2 \over 3}\overrightarrow {AB} \cr & \overrightarrow {PM} = \overrightarrow {PB} + \overrightarrow {BM} \cr & \,\,\,\,\,\,\,\,\,\, = {1 \over 3}\overrightarrow {AB} + {1 \over 4}\overrightarrow {BC} \cr & \,\,\,\,\,\,\,\,\,\, = {1 \over 3}\overrightarrow {AB} + {1 \over 4}\left( { - \overrightarrow {AB} + \overrightarrow {AC} } \right) \cr & \,\,\,\,\,\,\,\,\,\, = {1 \over {12}}\overrightarrow {AB} + {1 \over 4}\overrightarrow {AC} = {1 \over 4}\overrightarrow {AC} + {1 \over {12}}\overrightarrow {AB} \cr & Ta\,\,co:\,\,\,\overrightarrow {NP} = 8\overrightarrow {PM} \cr & \Rightarrow M,\,\,N,\,\,P\,\,thang\,\,hang. \cr} $$