# Dot product between two unit vectors

1. Nov 25, 2011

### Marioqwe

Hello, I am trying to find the angle between two unit vectors but I was wondering what I am supposed to do when the dot product is greater than 1 or less than -1.

For example

-0.0288067i + -0.989524j + -0.141463k
0.169194i + -0.0644865j + -0.983471k

2. Nov 25, 2011

### grzz

The unit vectors $\underline{i}$,$\underline{j}$and $\underline{k}$ all are at right angles to each other just like the x,y,and z co-ordinate axes.

Does your difficulty refer to the angle between two vectors which are not unit vectors?

3. Nov 25, 2011

### Marioqwe

The problem is that the dot product between the two vectors I mentioned above is less than -1, and that won't let me calculate the arccosine. I was wondering if there's another way of calculating the angle between them.

4. Nov 25, 2011

### Marioqwe

Nevermind !

5. Nov 25, 2011

### grzz

costheta = (v1 dot v2)/(magnitude of v1*magnitude of v2)

The above will always be greater than -1 and less than +1.

6. Nov 25, 2011

### Marioqwe

I'm sorry but once again, how would you deal with this vector?

0.444119i + 0.666155j + 0.599163k
-0.0587215i + 0.732467j + 0.678265k

the dot product is 1.73928, and the magnitude of each vector is 1. How do you calculate the angle between them? :(

7. Nov 25, 2011

### Rasalhague

Are you sure? I get a dot product of 0.868249 for these vectors, and 0.198062 for the vectors in your first post.

8. Nov 25, 2011

### HallsofIvy

It looks like you are just doing the dot product wrong. I get
(-0.0260793338585)+ (0.487936554385)+ (0.406391292195)= 0.8682485127215
just as Rasalhaque did.

Perhaps if you showed more detail on how you are doing the dot product we could see where your error is.

9. Nov 25, 2011

### grzz

Was this problem given as a 'punishment'? It is so tedious to calculate!

You must have a mistake in the calculations.

There is NO WAY that (v1 dot v2)/(magnitude of v1*magnitude of v2) is greater than 1 or less than -1.

10. Nov 25, 2011

### grzz

I have a feeling that Marioque is enjoying seeing us calculating!!

11. Nov 25, 2011

### grzz

I also got 0.8682484 for the dot product.

12. Nov 25, 2011

### Marioqwe

jaja! grzz. It was my mistake again :(. No more dumb questions. I'm really sorry.

13. Nov 25, 2011

### grzz

No need to be sorry. Sometimes I myself make mistakes.

My maxim is:

One may sometimes swallow some water but that is the way one learns to swim!