High School Angle between two vectors book problem

Click For Summary
The discussion centers on the angle between two vectors, P and Q, with a debate on whether it should be expressed as 180-θ or θ. The book states the angle is θ, which is supported by visualizing the vectors tail to tail, confirming that the angle is indeed θ. It is noted that the projection of vector Q along vector P is positive, suggesting the angle should be less than 90 degrees. The vectors OA and OB are referenced, reinforcing that the angle between them is θ. The conversation emphasizes the importance of understanding vector orientation and the implications of their projections.
gracy
Messages
2,486
Reaction score
83
triangular.jpg

Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
 
Physics news on Phys.org
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.
 
gracy said:
View attachment 100320
Should not angle between vector P and Q be 180-θ rather than θ? According to my book it is θ.
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).
 

Thread 'Does acceleration affect impact energy vs constant velocity?'

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...
View full post »

Similar threads

High School Confusion about the angle between two vectors in a cross product
  • · Replies 7 ·
Replies
7
Views
3K
Engineering Calculate angle between spacecraft & Sun vectors
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Finding the max angle of a longboard deck before the wheels slip
  • · Replies 8 ·
Replies
8
Views
2K
High School Are parallel vectors always in the same direction?
  • · Replies 9 ·
Replies
9
Views
4K
High School Calculating the perfect tennis shot using vectors
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Angles between 4-vectors in special relativity?
  • · Replies 5 ·
Replies
5
Views
1K
Finding the angle between two vectors
  • · Replies 2 ·
Replies
2
Views
1K
Suggestions for HS geometry book (proofs)
  • · Replies 14 ·
Replies
14
Views
2K
For a Pendulum: Knowing Acceleration Find Maximum Angle
  • · Replies 26 ·
Replies
26
Views
3K
Physical meaning of field components in "angle" directions
  • · Replies 2 ·
Replies
2
Views
1K