Vectors A and B are in the xy plane

In summary, the scalar product of vectors A and B in the xy plane is 20.0 units. Vector A makes a 27.4° angle with the x-axis and has a magnitude of 12.0 units, while vector B has a magnitude of 24.0 units. Using the equation cos(x)= a⋅b/(||a||⋅||b||), we can find that the possible angles for B are 113.4° and 301.4°.
  • #1
DoctorMathU
3
0

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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  • #2
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:
 
  • #3
image.jpeg
Okay, I only know for A.
 

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  • #4
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?
 
  • #5
DoctorMathU said:
But it gives me 86°, that's not the solution...
That's the angle between the two vectors.
 
  • #6
The relevant equation for the angle between A and B is cos(x)= a⋅b devided by ||a|| *||b||
 
  • #7
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.
 

1. What is the xy plane?

The xy plane is a two-dimensional coordinate system used in mathematics and science to plot points and represent vectors. It consists of a horizontal x-axis and a vertical y-axis, with the point of origin (0,0) at their intersection.

2. How are vectors A and B represented in the xy plane?

Vectors A and B are represented by arrows in the xy plane, with the tail of the vector starting at the origin and the head pointing to the coordinates of the vector. The length of the arrow represents the magnitude of the vector and the direction of the arrow indicates its direction.

3. Can vectors A and B be in the same position in the xy plane?

No, vectors A and B cannot be in the same position in the xy plane. Each vector has a unique position and direction in the plane, even if they have the same magnitude and direction.

4. How do you calculate the magnitude of vectors A and B in the xy plane?

The magnitude of a vector in the xy plane can be calculated using the Pythagorean theorem, where the magnitude is the square root of the sum of the squared x and y components of the vector. In other words, the magnitude is the length of the vector's arrow.

5. What is the difference between vectors A and B in the xy plane?

The difference between vectors A and B in the xy plane is their magnitude and direction. While both vectors may have the same position in the plane, they can have different lengths and point in different directions, making them distinct vectors.

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