Trong mặt phẳng tọa độ cho \(\overrightarrow a = (1 ; 2) ; \overrightarrow b = ( – 3 ; 1) ; \)\(\overrightarrow c = ( – 4 ; – 2)\).
Tính \(\overrightarrow a . \overrightarrow b ; \overrightarrow b . \overrightarrow c ; \overrightarrow c . \overrightarrow a ;\)\( \overrightarrow a .(\overrightarrow b + \overrightarrow c ) ; \overrightarrow a .(\overrightarrow b – \overrightarrow c ).\)
Giải
\(\begin{array}{l}\overrightarrow a .\overrightarrow b = 1.( – 3) + 2.1 = – 1 ;\\ \overrightarrow b .\overrightarrow c = 10 ; \overrightarrow c .\overrightarrow a = – 8 ;\\\overrightarrow a \left( {\overrightarrow b + \overrightarrow c } \right) = \overrightarrow a .\overrightarrow b + \overrightarrow a .\overrightarrow c = – 9 ;\\\overrightarrow a \left( {\overrightarrow b – \overrightarrow c } \right) = \overrightarrow a .\overrightarrow b – \overrightarrow a .\overrightarrow c = 7.\end{array}\)