Question

unu si doi va rog mult. dau funda.

Answer 1

E1.a)AB=OB-OA=3i+5j-2i-3j=i+2j
AB(1,2)
BC=OC-OB=-i+6j-3i-5j=-4i+j
BC(-4,1)
AC=OC-OA=-i+6j-2i-3j=-3i+3j
AC(-3,3)
b)OA+OB+OC=2i+3j+3i+5j-i+6j=4i+14j
c) AB+2CB-3AC=OB-OA+2OB-2OC-3OC+3OA=2OA+3OB-5OC=4i+6j+9i+15j+5i-30j=18i-9j
3OA+4BC=3OA+4OC-4OB=6i+9j-4i+24j-12i-20j=-10i+13j
d)AB+aBC+(2a-1)CA=0
OB-OA+aOC-aOB+(2a-1)OA-(2a-1)OC=0
(2a-2)(2i+3j)+(1-a)(3i+5j)+(-a+1)(-i+6j)=0
i(4a-4+3-3a+a-1)+j(6a-6+5-5a-6a+6)=0=>
2a-5=0=>a=5/2
E2.a)AB+CD=OB-OA+OD-OC=-3i+5j+2i+4j+5i-3j-3i-6j=7i
b) AB+2BC+3CD=OB-OA+2OC-2OB+3OD-3OC=-OA-OB-OC+3OD=-2i-4j+3i-5j-3i-6j+15i-9j=13i-24j
c) OA+3OD+5BC=OA+3OD+5OC-5OB=2i+4j+15i-9j+15i+30j+15i-25j=47i+18j