1.1.52 Vector Algebra

condition: It is known that the two sides of the triangle \( A B C \) are specified by the vectors \( \overline{A B}=2 \bar{p}-\bar{q} \) and \( \overline{A C}=3 \bar{p}+2 \bar{q} \), where \( |\bar{p}|=3,|\bar{q}|=1 \quad \) and \( \quad \) the angle between the vectors \( \bar{p} \) and \( \bar{q} \) is equal to \( \pi / 3 \); a) find the scalar product of the vectors \( \bar{p} \) and \( \bar{q} \); b) express the vector \( \overline{B C} \) in terms of the vectors \( \bar{p} \) and \( \bar{q} \); c) calculate the length of the median of the triangle \( A B C \) drawn from the vertex \( A \).