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gianeshwar
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Dear Friends! How can I find the minimum value of
sum of cosine of angles between three unit vectors in three dimension space
sum of cosine of angles between three unit vectors in three dimension space
Thank You Mathman! Actually I am interested to find minimum value not absolute . What I am thinking Geometrically is that the possibility seems by imagining unit vectors inclined at 120 degrees to each other in 3D space.Am I correct?It gives thevalue -3/2.mathman said:Are you interested in absolute value (easy = 0) or most negative (harder)?
You can put 3 vectors at 120 deg. apart in a plane. I haven't looked at the problem in any detail, but I would guess you could do better in 3d.gianeshwar said:Thank You Mathman! Actually I am interested to find minimum value not absolute . What I am thinking Geometrically is that the possibility seems by imagining unit vectors inclined at 120 degrees to each other in 3D space.Am I correct?It gives thevalue -3/2.
The purpose of finding the minimum value of the sum of cosine angles in 3D space is to determine the most efficient arrangement of vectors in 3D space. This is useful in various fields such as physics, engineering, and computer graphics.
The minimum value of the sum of cosine angles in 3D space is calculated by finding the dot product of the vectors and taking the inverse cosine of the result. This value will be the minimum value of the sum of cosine angles in 3D space.
The minimum value of the sum of cosine angles in 3D space represents the most optimal arrangement of vectors in terms of minimizing the overall angle between them. This can help in optimizing designs and improving efficiency in various applications.
No, the minimum value of the sum of cosine angles in 3D space cannot be negative. The range of cosine values is between -1 and 1, so the minimum value will always be equal to or greater than -1.
The number of vectors does not affect the minimum value of the sum of cosine angles in 3D space. The minimum value is solely dependent on the dot product of the vectors, not the number of vectors itself.