Задача 53595 ABCDEF — правильный шестиугольник, АВ =...

5f6c65a2019fbf2dafd19b19

24.09.2020 14:28:25

ABCDEF — правильный шестиугольник, АВ = р, ВС = q. Выразить через р и q векторы CD, DE, EF, FA, АС, AD, АЕ.

5f3ea7e3faf909182968ddd9

24.09.2020 14:48:07

★

1)
vector{DE}=-vector{AB}=-vector{p}
2)
vector{EF}=-vector{BC}=-vector{q}
3)
vector{AB}+vector{BC}+vector {CD}=vector{AD}
vector{AD}=2 vector{BC} =2 vector{q}

vector {CD}=vector{AD}-vector{AB}-vector{BC}=2 vector{BC} -vector{AB}-vector{BC}= vector{BC} -vector{AB}= vector{q} -vector{p}

4)
vector{FA}+vector{AB}+vector {BC}=vector{FC}
vector{FC}=2 vector{AB}=2 vector{p}

vector{FA}=vector{FC}-vector{AB}-vector {BC}=2 vector{AB}-vector{AB}-vector {BC}=vector{AB}-vector {BC}=vector{p}-vector {q}

vector {FA}=-vector {CD} можно и так

5)
vector{AD}=2 vector{BC} =2 vector{q}

6)
vector{AB}+vector{BC}=vector {AC}
vector {AC}=vector{p}+vector {q}