# Finding the magnitude of 2 vectors given the resultant

• Mallorie
In summary, the formula for finding the magnitude of 2 vectors given the resultant is |A + B| = √(A² + B² + 2ABcosθ), where A and B are the magnitudes of the two vectors and θ is the angle between them. To find the angle between two vectors, you can use the dot product formula: A · B = |A| * |B| * cosθ, where A and B are the two vectors and θ is the angle between them. Rearranging this formula, we get: θ = cos⁻¹((A · B) / (|A| * |B|)). Finding the magnitude of 2 vectors given the resultant is
Mallorie

## Homework Statement

The figure depicts the sum of two velocities, vA and vB. The value of the sum is7 m/s and the angles shown in the image are θ1 = 29.8°, and θ2 = 18.3°.

## The Attempt at a Solution

What a great diagram.

I'm sorry, did you want some help? You might want to mosey on over to the homework rules thread and take a gander. A complete problem statement would also be helpful.

## What is the formula for finding the magnitude of 2 vectors given the resultant?

The formula for finding the magnitude of 2 vectors given the resultant is:
|A + B| = √(A² + B² + 2ABcosθ), where A and B are the magnitudes of the two vectors and θ is the angle between them.

## How do you find the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula:
A · B = |A| * |B| * cosθ, where A and B are the two vectors and θ is the angle between them. Rearranging this formula, we get:
θ = cos⁻¹((A · B) / (|A| * |B|)).

## What is the importance of finding the magnitude of 2 vectors given the resultant?

Finding the magnitude of 2 vectors given the resultant is important because it allows us to determine the overall magnitude or size of the combined vectors. This can be useful in many scientific and engineering applications, such as calculating forces, velocities, and accelerations.

## Can the magnitude of 2 vectors given the resultant ever be negative?

No, the magnitude of 2 vectors given the resultant cannot be negative. The magnitude always represents a positive value, as it is a measure of the size or length of a vector.

## Are there any other methods for finding the magnitude of 2 vectors given the resultant?

Yes, there are other methods for finding the magnitude of 2 vectors given the resultant, such as using the Pythagorean theorem or using trigonometric functions. However, the formula mentioned in the first question is the most commonly used method.

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