Finding 3D vector component form given 3 points I am having a brain fart with a simple methodology here.
Say I have three points in 3 dimensions: 
(1,2,0) , (0,0,0) , and (-2,1,0)
The formula to find component form is < t point - i point > 
but my question is: What if the initial and terminal points are not specified as above?
How do we know which points to subtract and add from each correctly?
 A: The vertices of the triangle are given to be $A(1,2,0)$, $B(0,0,0)$ and $C(-2,1,0)$. The question asks us whether this triangle is acute, obtuse or right. 
Recall: A triangle is obtuse if any one angle of the triangle is obuse-angled. It is a right triangle if any one angle is a right angle. Finally, it is an acute triangle if all the three angles are acute. So to do the problem, we need to check whether each of the angles is acute or obtuse or right. I will show the steps for one angle. You can do for the other two angles similarly. 
First of all, let $\theta$ be some angle in $(0, \pi)$. Then


*

*$\theta$ is acute $\iff$ $\theta < \frac{\pi}{2}$ $\iff$ $\cos \theta > 0$.

*$\theta$ is right $\iff$ $\theta = \frac{\pi}{2}$ $\iff$ $\cos \theta = 0$.

*$\theta$ is obtuse $\iff$ $\theta > \frac{\pi}{2}$ $\iff$ $\cos \theta < 0$.


Now, to see if (say) angle $A$ of the triangle $ABC$ is acute/right/obtuse, we need to check whether $\cos \angle BAC$ is positive/zero/negative. But what is $\cos \angle BAC$? It is the angle made by the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$. (When you are computing the angle at a particular vertex $v$, you should make sure that both the vectors corresponding to the two adjacent sides have that vertex $v$ as the initial point.) We will first compute these two vectors:
$$
\overrightarrow{AB} = (0,0,0) - (1,2,0) = (-1,-2,0)
$$
$$
\overrightarrow{AC} = (-2,1,0) - (1,2,0) = (-3,-1,0)
$$
Therefore, the angle between these vectors is given by:
$$
\cos \angle BAC = \frac{\overrightarrow{AB} \cdot \overrightarrow{AC}}{|\overrightarrow{AB}| |\overrightarrow{AC}|}
= \ldots \tag{1}
$$
Can you take it from here? From the sign of this value, you should be able to decide if angle $A$ is acute/right/obtuse. 
Now, do the same procedure for the remaining two angles $B$ and $C$ as well. That should help you solve the problem. 
A shortcut. Since you are not interested in the actual values of the angles, but you need only whether they are acute, obtuse or right, it is enough to compute only the sign of the numerator (the dot product between the vectors) in formula (1). The denominator is always positive. 
A: In geometric problems like this, it's good to have an intuition of what sort of information would actually allow you to solve the problem.
For instance, you've already given one example: if you know the initial and final points on the vector, then there's really only one vector that can go between them. Those initial and final points specify that vector.
I don't know the exact problem you're trying to solve, but very often you don't have the final and initial points. Can you think of any other bits of information could you have that would specify the vector? 
Perhaps you've been given the magnitude of the vector, and also another vector in the same direction. In this case, there's only one vector with your given magnitude and pointing in the given direction. So magnitude plus direction also specify that vector.
Maybe there's some way in your question to figure out the magnitude and direction of the vector? If this is true, see if you can figure out how to find the vector, possibly using unit vectors... But before you dive into the maths, make sure you can see that all of your constraints actually specify one unique vector.
