# Dot product

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

nrqed
Homework Helper
Gold Member
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.

CompuChip
Homework Helper
<off-topic>
If you insist: False, just take a non-Euclidean metric.
</off-topic>

so is it true or false
and why????

thank you

nrqed
Homework Helper
Gold Member
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