# Cross Products isn't giving the right answer to angle.

Vectors in geometry

### Cross Products isn't giving the right answer to angle.

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?

Posts: 1
Joined: Mon Jan 14, 2008 6:19 am
Reputation: 0

Or write them here.

Here is 2 good articles:
http://www.math10.com/en/geometry/vecto ... ctors.html
http://www.math10.com/en/geometry/vecto ... tions.html

Look at the second carefully, please!

Math Tutor

Posts: 418
Joined: Sun Oct 09, 2005 11:37 am
Reputation: 32

### Re: Cross Products isn't giving the right answer to angle.

There is nothing wrong with the formula, gut you need to understand that the trig functions are not "one-to-one" so do not have true inverses. In particular, if x is a small number, sin(90+ x)= sin(90- x). Calculators typically give angles between -90 and 90 degrees ($$-\pi/2$$ to [/tex]\pi/2[/tex] radians) while it is clear that this answer is larger 90 degrees. It is not that the formula is wrong- you are using the calculator incorrectly.
Guest