Answer:
1) False
2) True
3) a) True b) False
4) False
Step-by-step explanation:
1)
Two-point are collinear if they lie in the same line. The vector -2AB is antiparallel to the vector AB then it is False.
2)
A unit vector could be difinede as:
[tex]\vec{u}=\frac{\vec{v}}{|\vec{v}|}[/tex]
Terefore, [tex]\frac{1}{AB}\vec{AB}[/tex] is a unit vector. It is True.
3)
a) If AB=-3AC
The points, A, B, and C are collinear, because all of them lie in the same line. True
b) Let's take the modulus in each side.
[tex]\vec{AB}=-3\vec{AC}[/tex]
[tex]|\vec{AB}|=|-3\vec{AC}|[/tex]
[tex]|\vec{AB}|=|-3||\vec{AC}|[/tex]
[tex]|\vec{AB}|=3|\vec{AC}|[/tex]
So it is False.
4)
If we put the vector AI = 3/2 AB into the first equation we will have:
[tex]2(-\frac{3}{2}\vec{AB})+3\vec{IB}=-3\vec{AB}+3\vec{IB}[/tex]
And we can not say that it is a cero vector, so it is False.
I hope it helps you!
