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

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To solve for the angles in a triangle defined by the vertices [2,-1,0], [5,-4,3], and [1,-3,2], it's essential to calculate the lengths of the sides by determining the distances between the points. The sum of the angles should equal 180 degrees, but using the dot product method has led to confusion, yielding a total of only 110 degrees. It's important to consider the direction of the vectors when calculating angles, as the angle between the tail of one vector and the head of another differs from the angle derived from the dot product. An alternative method is to apply the cosine rule after finding the side lengths, providing a purely geometrical solution. This approach can clarify the angle calculations and ensure they align with the triangle's properties.
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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.
 
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To find the angle between two vectors you can use

u\cdot v=|u||v|\cos{\theta}
 
I have tried this, but the sum of the three angles only equals 110 not 180.
 
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.
 
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.
 

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