# How Do You Compute the Flux of a Vector Field Through a Circle?

In summary, a scalar is a quantity with only magnitude, while a vector has both magnitude and direction. Vectors can be added by adding their corresponding components. Scalar multiplication allows for multiplication of a vector by a number, resulting in a vector with the same direction but a different magnitude. The magnitude of a vector can be found using the Pythagorean theorem. The dot product of two vectors is a scalar value calculated by multiplying the corresponding components of the vectors and adding them together.

## Homework Statement

Let C be the circle of radius 2 centered on the origin and contained in the plane 2x - 3y + 5 = 0. Compute the flux through C of the constant vector field v = {6, - 1, 12}

I have no idea about this problem. This is one the review problem which was given to us in the class for next week's exam.

Well, what is the definition (it involves an area integral) of flux of a vector field through a surface?

What is the surface in this case? What is the unit normal to that surface?

## What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction.

## How do you add vectors?

To add vectors, you must add their corresponding components. For example, to add two 2D vectors (x1, y1) and (x2, y2), you would add their x-components (x1 + x2) and their y-components (y1 + y2).

## Can vectors be multiplied?

Yes, vectors can be multiplied by a scalar (a number). This is known as scalar multiplication and it results in a vector with the same direction but a different magnitude.

## How do you find the magnitude of a vector?

The magnitude (or length) of a vector can be found using the Pythagorean theorem. For a 2D vector (x, y), the magnitude is equal to the square root of (x^2 + y^2).

## What is the dot product of two vectors?

The dot product of two vectors is a scalar value that represents the magnitude of one vector multiplied by the projection of the other vector onto it. This can be calculated by multiplying the corresponding components of the vectors and then adding them together.

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