# Vector Subtract Given Magnitude

• Lori
However, since C = A + (-B), we must subtract the magnitude of B from this result to get the magnitude of C. C = 45.83 - 50 = -4.17 In summary, the magnitude of vector C is -4.17.
Lori

## Homework Statement

Let's say i was given Vector A and B. The Angle between them is 60 degrees. Vector A's magnitude is 40 and Vector B's magnitude is 50. Find magnitude of vector C, if C = vector A - vector B.

## Homework Equations

I'm given the magnitudes, and need to find magnitude of C

## The Attempt at a Solution

I'm kinda confused cause I don't think this is a simple problem. But, I thought that magnitude of C would be 10. Since A-B = -10 , and 10 is the magnitude[/B]

Can you draw a diagram for the situation?

#### Attachments

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By which side of the triangle the vector A-B is represented? What do you get if you properly use law of cosines?

Magnitudes don't add that way unless the vectors are parallel and so you need to solve the triangle using the law of cosines.

For example, if the angle between A and B were 0, then by the law of cosines

$$c^2=a^2+b^2-2ab\cos{(0)}= (a-b)^2 \\ c = |a-b|$$

Which is what you tried to do but the angle is not zero in this case which is why it's wrong

Lori
RedDelicious said:
Magnitudes don't add that way unless the vectors are parallel and so you need to solve the triangle using the law of cosines.

For example, if the angle between A and B were 0, then by the law of cosines

$$c^2=a^2+b^2-2ab\cos{(0)}= (a-b)^2 \\ c = |a-b|$$

Which is what you tried to do but the angle is not zero in this case which is why it's wrong
Thanks. I definitely did not learn this from my physics class.

I thought of this problem as C = A + (-B). This means that it is the same as adding a vector, just the vector you are adding is negative. In order to add the vectors, we must split them into their components. We know that vector A is at an angle of 60 and therefore has X and Y components, while B is parallel to the horizontal and only has an X component equal to its magnitude.

To split vector A, we use Cos and Sin to find the vertical and horizontal components of the vector.
X Component (horizontal): Cos(60)*40=20
Y Component (vertical): Sin(60)*40=34.64

Now that we know the vertical and horizontal components of vector A, we can add the corresponding components of B, although since we are ultimately subtracting B from A, we just make B negative.

This leaves us with:
X: 20 + (-50) = -30
Y: 34.64 + 0 = 34.64

Then we use the Pythagorean theorem to find the result vector of these new horizontal and vertical components
(A*A) + (B*B) = (C*C) = √(-30*-30) + (34.64*34.64) = C
C = 45.83

We know that the resultant vector has a magnitude of 45.83.

## What is vector subtraction given magnitude?

Vector subtraction given magnitude is a mathematical operation used to find the difference between two vectors with known magnitudes. It involves subtracting the components of one vector from the corresponding components of the other vector.

## How is vector subtraction given magnitude different from regular vector subtraction?

Regular vector subtraction involves subtracting two vectors with unknown magnitudes and directions. Vector subtraction given magnitude only requires the knowledge of the magnitudes of the two vectors, making it easier to calculate.

## What are the steps involved in vector subtraction given magnitude?

The steps involved in vector subtraction given magnitude are: 1) Determine the magnitudes of the two vectors, 2) Identify the components of each vector, 3) Subtract the components of one vector from the corresponding components of the other vector, 4) Write the resulting vector in component form.

## Can vector subtraction given magnitude result in a negative vector?

Yes, vector subtraction given magnitude can result in a negative vector. This can happen when the magnitude of one vector is greater than the magnitude of the other vector, and the subtraction of the smaller vector from the larger vector results in a negative value for one or more components.

## What is the significance of vector subtraction given magnitude in science?

Vector subtraction given magnitude is an important tool in science, particularly in physics and engineering. It allows scientists to find the difference between two vectors with known magnitudes, which is useful in calculating forces, velocities, and other physical quantities.

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