How do I solve triangles in 3D with specific vertices?

[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.

 

[nicksauce]

To find the angle between two vectors you can use

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

 

[uf2010]

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

 

[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.

 

[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.