Dot product between two unit vectors

  • Thread starter Marioqwe
  • Start date
  • #1
68
4
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

  • #2
993
13
... I am trying to find the angle between two unit vectors ...
The unit vectors [itex]\underline{i}[/itex],[itex]\underline{j}[/itex]and [itex]\underline{k}[/itex] 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
68
4
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
68
4
Nevermind !
 
  • #5
993
13
costheta = (v1 dot v2)/(magnitude of v1*magnitude of v2)

The above will always be greater than -1 and less than +1.
 
  • #6
68
4
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
1,384
2
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.
 
  • #8
HallsofIvy
Science Advisor
Homework Helper
41,833
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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
993
13
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
993
13
I have a feeling that Marioque is enjoying seeing us calculating!!
 
  • #11
993
13
I also got 0.8682484 for the dot product.
 
  • #12
68
4
jaja! grzz. It was my mistake again :(. No more dumb questions. I'm really sorry.
 
  • #13
993
13
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!
 

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