# Dot product between two unit vectors

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

## Answers and Replies

... I am trying to find the angle between two unit vectors ...

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?

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.

Nevermind !

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

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

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? :(

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? :(

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

HallsofIvy
Homework Helper
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.

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.

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

I also got 0.8682484 for the dot product.

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

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!

Enjoy your 'swimming' in PhysicsForums!