120градусів
Объяснение:
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Объяснение:5) ↑а(4;3), ↑b(6;-8). ↑с(m;6)
а)Пусть α-угол между векторами ↑а и ↑b , тогда a·b= |a| |b|· Cosα
a·b = 4·6+ 3·(-8)= 24-24=0 . Так как скалярное произведение векторов равно 0, то вектора перпендикулярны, значит α=90°
б)↑а(4;3), ↑с(m;6) коллинеарны, значит их координаты пропорциональны, т.е. 4/m= 3/6 ⇒3m=24 ⇒m=8
b) ↑b(6;-8). ↑с(m;6) перпендикулярны, значит их скалярное произведение равно нулю, т.е. 6m+(-48)=0 ⇒6m=48 ⇒ m=8
6) A(1;1), В(2;3), С(0;4), Д(-1;2)
Воспользуемся признаком параллелограмма
Если в четырехугольнике противоположные стороны попарно равны, то этот четырехугольник — параллелограмм.
АВ²= (1-2)²+(1-3)²= 1+4=5;
ВС²= (2-0)²+(3-4)²=4+1=5;
СД²= (0+1)²+(4-2)²=1+4=5;
АД²= (1+1)²+(1-2)²=4+1=5 ⇒ АВ=СД, ВС=АД ⇒ АВСД параллелограмм
