- #1
gracy
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Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
Angle between two vectors book problem
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SUMMARY
The angle between vectors P and Q is definitively θ, as established in the discussion. The reasoning is based on the projection of vector Q along vector P, which indicates that the angle remains less than 90 degrees when the vectors are positioned tail to tail. The discussion also clarifies that the parallelogram construction is merely a visual aid, and the vectors OA and OB directly define the angle θ between them. The confusion regarding the angle being 180-θ is addressed, confirming that θ is the correct measurement according to the referenced book.
PREREQUISITES- Understanding of vector notation and representation
- Familiarity with vector projections
- Knowledge of geometric constructions involving vectors
- Basic trigonometry related to angles
- Study vector projection techniques in depth
- Explore geometric interpretations of vector angles
- Learn about the properties of parallelograms in vector addition
- Investigate the relationship between vector angles and coordinate axes
Students studying physics or mathematics, educators teaching vector concepts, and anyone seeking to clarify vector angle relationships in geometric contexts.
Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
- #2
nasu
Homework Helper
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If you put them tail to tail you can see that the angle is theta. Actually OB is the vector Q translated so that it has same origin as P.
Another way to look at it is that the projection of Q along P is in the positive direction so the angle should be less than 90 degrees.
All this assumes that the vector Q is from A to C. It does not have an arrow in the drawing.
Another way to look at it is that the projection of Q along P is in the positive direction so the angle should be less than 90 degrees.
All this assumes that the vector Q is from A to C. It does not have an arrow in the drawing.
- #3
sophiecentaur
Science Advisor
Homework Helper
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The parallelogram is just a 'construction'. The vectors are OA and OB, which makes the angle between them θ. Another way of looking at it is to consider the difference between the respective angles of each vector and the X axis (or any other axis).gracy said:
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