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

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Homework Help Overview

The discussion revolves around the conditions under which a dot product of two vectors can be negative, specifically focusing on the relationship between the angle between the vectors and the sign of the dot product.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the formula for the dot product, ABcos(theta), and question the validity of the statement regarding angles larger than 90 degrees leading to a negative result. Some participants present counterexamples and discuss the conventional understanding of angle ranges in vector analysis.

Discussion Status

The discussion is ongoing, with participants expressing differing views on the statement's truthfulness. Some suggest that the conventional interpretation of angles in the context of dot products should be considered, while others challenge this interpretation. There is no explicit consensus reached yet.

Contextual Notes

Participants note that the angle is typically considered within the range of 0 to π, which may influence the understanding of the dot product's behavior. There is mention of non-Euclidean metrics, indicating a broader context for the discussion.

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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