Angle between Vector question

In summary, in order for the magnitude of A + B to be 100 times larger than the magnitude of A - B, the angle between the two vectors must be 90 degrees. This can be determined by setting the scalar product between A+B and A-B to 0, since the two vectors are perpendicular. Using the geometrical and trigonometric properties of vectors, the length of A+B can be set to 100 times the length of A-B, and the angle between them can be solved for as 90 degrees.
  • #1
moonworn
2
0

Homework Statement


Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A + B to be 100 times larger than the magnitude of A - B, what must be the angle between them?


Homework Equations





The Attempt at a Solution



I am completely lost. Vectors are a completely new subject to me. I am not familiar with vector algebra notation yet as we haven't yet covered it, but I assume we are to solve this visually/conceptually given what we do know. Any help where to start?
 
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  • #2
HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

Daniel.
 
  • #3
Hrm maybe if I had a step by step explanation I would understand what was going on. I didn't even know what "vector" was yesterday. I appreciate the hint daniel, but I still have no idea.
 
  • #4
HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

Sorry... A and B are not perpendicular

EDIT:

Hints: |A+B| = 100 |A-B|

notice |A+B|^2 = (A+B) dot (A+B) and
A dot B = |A| |B| cos \theta
 
Last edited:
  • #5
dextercioby said:
HINT: The scalar product between A+B and A-B is 0, since the 2 vectors are perpendicular.

This seems backwards: actually A+B and A-B are perpendicular (i.e. they have scalar product zero) because A and B are equal magnitude.

Moonworm, if you are just starting vectors, draw a diagram with two vectors from a point, with equal magnitude, and an angle theta between them. Then draw the vectors a+b (using the parallelogram rule) and a-b.

You can find the lengths of a+b and a-b using geometry and trig.
 

1. What is the angle between two vectors?

The angle between two vectors is the measure of the amount of rotation that is needed to align one vector with the other vector. It is measured in degrees or radians.

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

To calculate the angle between two vectors, you can use the dot product formula: θ = cos⁻¹((a · b) / (|a| * |b|)), where a and b are the two vectors and |a| and |b| represent their magnitudes. Alternatively, you can use the cross product formula: θ = sin⁻¹(|a × b| / (|a| * |b|)), where a and b are the two vectors and |a| and |b| represent their magnitudes.

3. What is the difference between the angle between two vectors and the angle of a vector?

The angle between two vectors is the measure of the rotation needed to align one vector with the other, while the angle of a vector is the measure of the rotation of the vector from its initial position to its final position. The angle of a vector is always positive, while the angle between two vectors can be positive or negative depending on the direction of rotation.

4. Can the angle between two vectors be greater than 180 degrees?

No, the angle between two vectors cannot be greater than 180 degrees. This is because 180 degrees represents a straight line, and any rotation beyond that would result in a negative angle, which is not possible.

5. How is the angle between two vectors used in real-world applications?

The angle between two vectors is used in various fields such as physics, engineering, and computer graphics. It is used to calculate the work done by a force, determine the direction and magnitude of a resultant force, and to create 3D models and animations in computer graphics. It is also used in navigation to determine the direction of travel and in robotics to calculate the orientation of objects.

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