Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#1 2008-01-13 22:05:07
- ConfusedAboutCrossProduct
- Member
- Registered: 2008-01-13
- Posts: 2
Cross Products isn't giving the right answer to angle.
Hi,
When I use cross products to find an angle of 2 vectors as compared to using dot products, I realised that it's wrong.
Using dot products to find angle
===================================
V = (-3, 1, 0)
W = (1,2,0)
Formula: cosΘ = V dot W /( |V||W| )
=> cosΘ = -1 / √50
=> cosΘ = -0.141421
Inverse of cos gives 98.13° which is the correct angle.
Using cross products to find angle
===================================
V = (-3, 1, 0)
W = (1,2,0)
Formula: |VxW| = |V||W|sinΘ
=> sinΘ = |VxW| / |V||W|
=> sinΘ = 7 / √50
=> sinΘ = 0.989949
Inverse of sin gives 81.869898° which is a wrong angle.
But if 180°-81.869898° gives the right answer.
Why is that so? Is it something wrong with the formula?
Please advice, thank you so much for your time.
Last edited by ConfusedAboutCrossProduct (2008-01-13 22:06:07)
Offline
#2 2008-01-14 01:19:20
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Cross Products isn't giving the right answer to angle.
sin (81.9...) = sin (98.1...).
In fact, sin (x) = sin (180-x), for any x you might choose.
So 98.1... is also the inverse sin of your number, but your calculator tells you the lowest one.
Dot products don't run into that problem because inverse cos only has one value between 0 and 180.
Why did the vector cross the road?
It wanted to be normal.
Offline
#3 2008-01-14 03:24:09
- ConfusedAboutCrossProduct
- Member
- Registered: 2008-01-13
- Posts: 2
Re: Cross Products isn't giving the right answer to angle.
Hi mathsyperson, thank you for your reply.
Does that mean everytime if I use cross products to find angle I must always apply 180-x otherwise the answer will be wrong in term of degree?
If so, it seems like dot products is more precise in this.
Is there any significant advantage over dot products when using cross products to find angle?
Is there any instance where one can only use cross products to find angle of two vectors?
Offline
#4 2008-01-14 05:51:10
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Cross Products isn't giving the right answer to angle.
Hi mathsyperson, thank you for your reply.
Does that mean everytime if I use cross products to find angle I must always apply 180-x otherwise the answer will be wrong in term of degree?
It's not that simple, I'm afraid. If your calculator tells you that the angle is x, then the angle is actually one of x or 180-x, but you don't know which without doing more work.
Why did the vector cross the road?
It wanted to be normal.
Offline