# Solving for the Angle Between Vectors A and B

• LVanderlinden
In summary, the problem asks to determine the angle between two vectors A and B with equal magnitudes of 15.0, given that their sum is the vector 4.55 j. The suggested solution involves using the dot product formula ({\bf A} + {\bf B})\bullet({\bf A} + {\bf B}) and sketching the vectors to find the magnitude of the sum as a function of the angle. It is also suggested to simplify the equation by aligning the y-axis with the resultant vector.

#### LVanderlinden

1. Homework Statement

Vectors A and B have equal magnitudes of 15.0. If the sum of A and B is the vector 4.55 j, determine the angle between A and B.

3. The Attempt at a Solution

Try looking at

$$({\bf A} + {\bf B})\bullet({\bf A} + {\bf B})$$

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It helps if you show how you have attempted it.

Have you tried sketching two equal magnitude vectors with some arbitrary angle between them, then working out the equation for the magnitude of the sum as a function of the angle? (there is a simplification if you put the y-axis along the resultant vector.)

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## What is the formula for finding the angle between two vectors A and B?

The formula for finding the angle between vectors A and B is given by:
θ = cos-1 (A·B / |A||B|)
where A·B represents the dot product of vectors A and B, and |A| and |B| represent the magnitudes of vectors A and B, respectively.

## How do you calculate the dot product of two vectors?

The dot product of two vectors A and B is calculated by multiplying the corresponding components of the vectors and then summing the results.
In equation form, it can be represented as:
A·B = A1B1 + A2B2 + ... + AnBn
where n represents the number of dimensions of the vectors.

## Can the angle between two vectors ever be negative?

No, the angle between two vectors is always positive. It is measured in the counterclockwise direction and ranges from 0 to 180 degrees.

## What is the range of possible values for the angle between two vectors?

The angle between two vectors can range from 0 degrees (when the vectors are parallel) to 180 degrees (when the vectors are antiparallel). Any value in between represents an acute or obtuse angle.

## What is the significance of finding the angle between two vectors?

Finding the angle between two vectors is important in understanding the relationship between the two vectors. It can help determine if the vectors are parallel, perpendicular, or at an angle to each other. It is also useful in many applications in physics and engineering, such as calculating forces and velocities.