# Simple vector problems (hints please)

sony
Hi, I'm stuck here:

P1(1,2,3) and P2(2,2,2)
Q1: Find a unitvector that points from P1 to P2. - A unitvector is a vector with length 1, right? But then what...?

Q2: A point M lies on the center on the line from P1 to P2. What is the position vector to M?

The sides of a parallellogram are a=2i-j+k and b=i+j
Q3: Find two vector that make up the diagonals. - I don't have a clue, which sides are a and b? And WHY! does my crappy book insist on writing everything with "i, i and k" thus making everything more difficult to read. (In HS we had fx: AB=[2,5,1]...)

Thanks for hints!

H_man
If you subtract the coordinates of point p2 from point p1 you will have your vector $$V_1_2$$.

You are correct, any unit vector does have a magnitude of one.

You create your unit vector by dividing $$V_1_2$$ by the magnitude of the vector.

Thus it will have magnitude one but the direction of the vector.

The other questions are solved in a similar manner.

sony
Ok, thanks :)

But I'm still stuck with the last to questions

H_man
Okay, as for the second one if we take a 1-D case this will simplify things. So if we have $$X_1$$ and $$X_2$$ then the point halfway between the two is clearly $$( X_1 + X_2 )/2$$.

Now just apply this to each coordinate for the halfway point for P1 and P2.

Your book is correct to use that coordinate system and you should just get used to it. Think of i = x, j = y and k = z in your head until you get used to it.

As for the 3rd one... draw a rough picture and see if u can make sense of it.

sony
Thanks I got that right now. But I'm unsure about the last one. I'm not even sure how to sketch it... I mean, one is in 3D and on in 2D...