Consider the points in . Determine the cosines of the angles of the triangle whose vertices are on these points.

Let denote the angle between and , let denote the angle between and and let denote the angle between and . Then we compute the cosines,

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Stumbling Robot

A Fraction of a Dot
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Determine the cosines of the angles of the triangle formed by *(2,-1,1), (1,-3,-5), (3,-4,-4)*

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Consider the points in . Determine the cosines of the angles of the triangle whose vertices are on these points.

Let denote the angle between and , let denote the angle between and and let denote the angle between and . Then we compute the cosines,

The answer is incorrect here. As Refael says, one needs to take differences between vectors. Then you also need to align vectors in such a way that every pair of vectors originates from the same point: BC vs BA, AB vs AC, and CA vs CB: the sum of the angles has to be pi in a triangle.

That reasoning is wrong. Let A, B and C the given vectors. So, what we want is the angle between the vectors B-C and A-C, B-A and C-A, C-B and A-B.