Vectors A and B are in the xy plane

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Homework Help Overview

The discussion revolves around the scalar product of two vectors, A and B, in the xy plane. The original poster provides specific magnitudes and angles for vector A and seeks to determine the possible directions of vector B based on the given scalar product.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the scalar product formula and its implications for determining the angle between the vectors. There are attempts to calculate the angle, with some participants expressing uncertainty about their results and seeking clarification on the relevant equations.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and interpretations. Some have suggested drawing diagrams to aid understanding, while others are questioning the assumptions made regarding the angles and the setup of the problem.

Contextual Notes

There is mention of a potential misunderstanding regarding the angle calculated and its relevance to the direction of vector B. Participants are encouraged to provide sketches to clarify their reasoning.

DoctorMathU
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Homework Statement


Vectors A and B are in the xy plane and their scalar product is 20.0 units. If Amakes a 27.4° angle with the x-axis and has magnitude A=12.0 units and B has magnitude B= 24.0 units, what can you say about the direction of B?
Answer: 113.4° and 301.4°

The Attempt at a Solution


I am not really good at vectors, so i just did the basic stuff like, cos(x)= a⋅b/(||a||⋅||b||)
But it gives me 86°, that's not the solution...
 
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DoctorMathU said:

Homework Statement


Vectors A and B are in the xy plane and their scalar product is 20.0 units. If Amakes a 27.4° angle with the x-axis and has magnitude A=12.0 units and B has magnitude B= 24.0 units, what can you say about the direction of B?
Answer: 113.4° and 301.4°

The Attempt at a Solution


I am not really good at vectors, so i just did the basic stuff like, cos(x)= a⋅b/(||a||⋅||b||)
But it gives me 86°, that's not the solution...
Welcome to the PF. :smile:

It usually helps to draw a diagram with the vectors on it to help you set up the calculation. Can you Upload a JPEG copy of your sketch? :smile:
 
image.jpeg
Okay, I only know for A.
 

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DoctorMathU said:
View attachment 215817 Okay, I only know for A.
What is the Relevant Equation for the scalar product? What does that then tell you about the angle between A and B?
 
DoctorMathU said:
But it gives me 86°, that's not the solution...
That's the angle between the two vectors.
 
The relevant equation for the angle between A and B is cos(x)= a⋅b devided by ||a|| *||b||
 
DoctorMathU said:
The relevant equation for the angle between A and B is cos(x)= a⋅b devided by ||a|| *||b||
Did you understand Doc Al's comment?
Doc Al said:
That's the angle between the two vectors.
You should be able to update your diagram with the possible positions for the B vector now... Please upload your updated diagram. Thanks.
 

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