Finding an angle between two vectors

In summary, the task was to find the angle between two given vectors u and v. Using the equation theta = arccos(u . v)/(|u||v|), the calculated angle was 70.068 degrees. However, the online assignment marked it as incorrect. It was suggested that the answer may be in radians, but since it was a webwork assignment, it could not be confirmed. It is important to note that angles are usually in radians unless stated otherwise.
  • #1
doublemint
141
0

Homework Statement



Find the angle between the vectors u=[4 -4 -3] and v=[2 2 -3].


Homework Equations



theta = arccos(u . v)/(|u||v|)


The Attempt at a Solution



arccos[(8+(-8)+9)/(sqrt(41)*sqrt(17))]= 70.068 degrees. According to the online homework, it is wrong...and I and stumped.
Any help would be appreciated!

Thanks!
 
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  • #2
Check if their answer isn't perhaps in radians.
 
  • #3
Well the thing is, it is a webwork assignment, so you can't really check the answer. And the question was not specfic for degrees or radians.:frown: Well, what counts is that I know I did it right. Thanks phyzmatix
 
  • #4
As a rule of thumb (well, this definitely holds for where I'm studying anyway) angles are ALWAYS in radians, unless specifically stated otherwise. It took me a while to get used to this also as we never did radians in school.
 

1. What is an angle between two vectors?

An angle between two vectors is the measurement of the amount of rotation needed to align one vector with the other. It is usually measured in degrees or radians.

2. How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula or the cross product formula. The dot product formula is: θ = cos^-1 (u · v / |u||v|), where u and v are the two vectors. The cross product formula is: θ = sin^-1 (|u x v| / |u||v|), where u and v are the two vectors.

3. Can the angle between two vectors be negative?

Yes, the angle between two vectors can be negative. This happens when the two vectors are pointing in opposite directions and the angle between them is greater than 180 degrees. In this case, the angle can be represented as a negative value or as a value greater than 180 degrees.

4. What is the range of the angle between two vectors?

The range of the angle between two vectors is typically between 0 and 180 degrees, or 0 and π radians. However, if the vectors are in a three-dimensional space, the range can be between 0 and 360 degrees, or 0 and 2π radians.

5. Can the angle between two vectors be greater than 90 degrees?

Yes, the angle between two vectors can be greater than 90 degrees. This means that the vectors are not pointing in the same direction and are not perpendicular to each other. The angle can be as large as 180 degrees, which would mean that the two vectors are pointing in completely opposite directions.

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