Question

Cho Δ ABC tìm điểm I sao cho

\(a,3\overrightarrow{IA}+2\overrightarrow{IC}=\overrightarrow{0}\)

\(b,\overrightarrow{2IA}+\overrightarrow{3IB}=\overrightarrow{3BC}\)

\(c,\overrightarrow{IA}+\overrightarrow{IB}+2\overrightarrow{IC}=\overrightarrow{0}\)

Answer 1

a) Ta có:

\(3\overrightarrow{IA}+2\overrightarrow{IC}=\overrightarrow{0}\)

\(\Leftrightarrow3\overrightarrow{IA}=-2\overrightarrow{IC}\)

\(\Leftrightarrow3\overrightarrow{IA}=-2\left(\overrightarrow{IA}-\overrightarrow{CA}\right)\)

\(\Leftrightarrow3\overrightarrow{IA}=-2\overrightarrow{IA}+2\overrightarrow{CA}\)

\(\Leftrightarrow3\overrightarrow{IA}+2\overrightarrow{IA}=2\overrightarrow{CA}\)

\(\Leftrightarrow5\overrightarrow{IA}=2\overrightarrow{CA}\)

\(\Leftrightarrow\overrightarrow{IA}=\frac{2}{5}\overrightarrow{CA}\)