Cho tam giác ABC , trung tuyến AM . Khi đó vecto AB ⋅ vecto AC = AM^2 − k BC^2 . Vậy k = ?

Ta có:

\(\begin{array}{l}\overrightarrow {AB}  \cdot \overrightarrow {AC}  = \frac{{{{(\overrightarrow {AB}  + \overrightarrow {AC} )}^2} - {{(\overrightarrow {AB}  - \overrightarrow {AC} )}^2}}}{4}\\ = \frac{{4A{M^2} - B{C^2}}}{4} = A{M^2} - \frac{1}{4}B{C^2}.\end{array}\)