1.1.52 Vector Algebra

Condition: it is known that the two sides of the triangle \ (a b c \) are set by 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} \) equal \ (\ pi / 3 \); a) Find the scalar product of vectors \ (\ bar {p} \) and \ (\ bar {q} \); b) express the vector \ (\ overline {b c} \) through vectors \ (\ bar {p} \) and \ (\ bar {q} \); c) calculate the length of the median of the triangle \ (a b c \), drawn from the top \ (a \).