Sloving triangles in 3d

1. Sep 11, 2008

uf2010

How do i find the angles in the triangle with the vertices at [2,-1,0], [5,-4,3], and [1,-3,2]. This problem has been bothering me because when i find the angle between the vectors it only adds to roughly 110 degrees, and that cannot be right.

2. Sep 11, 2008

nicksauce

To find the angle between two vectors you can use

$$u\cdot v=|u||v|\cos{\theta}$$

3. Sep 11, 2008

uf2010

I have tried this, but the sum of the three angles only equals 110 not 180.

4. Sep 11, 2008

Defennder

nicksauce's approach should work here. You should be careful of the directions the vectors point and the angle between them. The angle between the tail of a vector and and the head of another vector is not the same as the one given by the dot product.

5. Sep 12, 2008

Defennder

Another way which doesn't involve vectors would be to find the lengths of the triangle by calculating distance between points, then apply cosine rule. A purely geometrical approach.