Get a negative dot product is to have an angle larger than 90 degrees.

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SUMMARY

The discussion centers on the conditions for obtaining a negative dot product between two vectors, specifically addressing the statement that this occurs only when the angle between them exceeds 90 degrees. Participants clarify that while it is commonly accepted that angles greater than 90 degrees yield a negative dot product, the cosine function can yield positive values in certain ranges, such as from 3π/2 to 2π. The consensus is that the statement is misleading as it does not account for the full range of angles and contexts, particularly in non-Euclidean metrics.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with the dot product formula (ABcos(theta))
  • Knowledge of trigonometric functions and their properties
  • Basic concepts of Euclidean and non-Euclidean geometry
NEXT STEPS
  • Study the properties of the dot product in vector mathematics
  • Learn about the cosine function and its behavior in different quadrants
  • Explore non-Euclidean geometry and its implications on vector operations
  • Investigate the concept of angles in vector analysis, particularly in higher dimensions
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Mathematicians, physics students, computer graphics developers, and anyone involved in vector analysis or trigonometry.

StephenDoty
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True or False:

The only way to get a negative dot product is to have an angle larger than 90 degrees.

The formula is ABcos(theta)

False because from 3pi/2 to 2pi the cos is positive and 3pi/2 and 2pi is larger than 90 degrees.

Right?

Stephen
 
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StephenDoty said:
True or False:

The only way to get a negative dot product is to have an angle larger than 90 degrees.

The formula is ABcos(theta)

False because from 3pi/2 to 2pi the cos is positive and 3pi/2 and 2pi is larger than 90 degrees.

Right?

Stephen

Usually it is understood that the angle is limited to be in the range 0 to Pi. In other words, one usually always use the smallest angle between the two vectors (if the angle on one side is above Pi, one starts using the angle on the other side). because of that, most people would agree with the statement given above.
 
<off-topic>
If you insist: False, just take a non-Euclidean metric.
</off-topic>
 
so is it true or false
and why?

thank you
 
StephenDoty said:
so is it true or false
and why?

thank you

I meant to say that most people would say that it's true that "The only way to get a negative dot product is to have an angle larger than 90 degrees"
 
1. The only way to get a negative dot product is to have an angle larger than 90 degrees.

2. because from 3pi/2 to 2pi the cos is positive and 3pi/2 and 2pi is larger than 90 degrees.

The second statement is NOT in contradiction with the first. The first statement does not say that ALL angles larger than 90 degrees give a negative dot product
 

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