# Which of the following transform as components of a 2d vector?

• briteliner
In summary, a 2d vector is a mathematical object with both magnitude and direction in a two-dimensional space. Its components are the two values that represent its magnitude and direction, typically described as the horizontal and vertical distances or x and y coordinates. To find the components, trigonometric functions such as sine and cosine can be used. The components can change depending on the vector's direction and magnitude, and are represented mathematically as a pair of numbers.
briteliner

## Homework Statement

which of the following pairs of quantities transform under rotations of the axes as the components of a two-dimensional vector?
a) (x2, -x1)
b) (x2,x1)
c) ((x1)^2,(x2)^2)

## The Attempt at a Solution

Dont know where to start. i'd appreciate just a little guidance :)

I'm not quite sure what you mean by that. If you mean does the transformation L((x1,x2))=(x2,-x1) (for a)) correspond to a rotation by some angle theta, look at the formula in your other post and see if it corresponds to some value of theta.

## 1. What is a 2d vector?

A 2d vector is a mathematical object that has both magnitude and direction in a two-dimensional space. It is often represented as an arrow with a length and a direction.

## 2. What are the components of a 2d vector?

The components of a 2d vector are the two values that represent its magnitude and direction. These values can be described as the horizontal and vertical distances or the x and y coordinates.

## 3. How do you find the components of a 2d vector?

To find the components of a 2d vector, you can use trigonometric functions such as sine and cosine. The horizontal component is calculated by multiplying the magnitude by the cosine of the angle, and the vertical component is calculated by multiplying the magnitude by the sine of the angle.

## 4. Can the components of a 2d vector change?

Yes, the components of a 2d vector can change depending on the direction and magnitude of the vector. If the vector is rotated or stretched, its components will also change.

## 5. How are the components of a 2d vector represented mathematically?

The components of a 2d vector can be represented mathematically as a pair of numbers, such as (x, y) or (a, b). The order of the numbers typically corresponds to the horizontal and vertical components respectively.

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