Vector Addition Question: find angle (A+B & A-B)

In summary, the conversation is discussing the angle between two vectors, A and B, with equal magnitudes. The goal is to find the angle that will result in the magnitude of A + B being 65 times greater than the magnitude of A - B. The person has attempted to use the dot product to solve for the angle, but is unsure if their math is correct and is looking for further clarification.
  • #1
alexi_b
49
1
Member has been warned to show more of their own effort.

Homework Statement


Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them?

Homework Equations

The Attempt at a Solution


I tried using the dot product and solving for the angle but i don't know if my math was right. I keep getting a relatively small angle which I know is around the right answer but its still off somehow. Please help!
 
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  • #2
Try something like A = a + jb, where a and b are the components of A.
 
  • #3
magoo said:
Try something like A = a + jb, where a and b are the components of A.

can you elborate? I am not quite sure what you mean
 
  • #4
alexi_b said:
I tried using the dot product and solving for the angle but i don't know if my math was right. I keep getting a relatively small angle which I know is around the right answer but its still off somehow.
Please post your working. We can rarely tell where you are going wrong from a rough outline.
 

1. What is vector addition?

Vector addition is a mathematical operation used to combine two or more vectors into a single vector. It involves adding the corresponding components of each vector to find the resulting vector's magnitude and direction.

2. How do you find the angle of vector addition?

To find the angle of vector addition, you can use the trigonometric functions cosine and sine. First, find the magnitude of the resulting vector using the Pythagorean theorem. Then, use the inverse tangent function to find the angle between the resulting vector and the horizontal axis.

3. What is the difference between A+B and A-B in vector addition?

A+B represents the sum of two vectors, while A-B represents the difference between two vectors. In other words, A+B is finding the resulting vector when adding two vectors together, while A-B is finding the resulting vector when subtracting one vector from another.

4. Can you use vector addition with more than two vectors?

Yes, vector addition can be used with any number of vectors. The process is the same as adding two vectors - you simply add the corresponding components of each vector to find the resulting vector's magnitude and direction.

5. How is vector addition used in science?

Vector addition is used in many scientific fields, including physics, engineering, and mathematics. It can be used to represent forces, velocities, and other physical quantities that have both magnitude and direction. It is also used in calculations involving displacement, velocity, and acceleration.

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