Question

What is the set of all vectors in R² whose second component is the cube of the first?

Answer 1

The set of all vectors in R² whose second component is the cube of the first is represented as -3/4�+�7/4�³.

Step-by-step explanation:

A vector in ℝ2 with the second component being the cube of the first component can be represented as −3/4�+�7/4�3, where � represents any scalar value.

Answer 2

The set of all vectors in R² with the second component as the cube of the first follows the form (x, x³). Their magnitude can be calculated using the Pythagorean theorem as R = √(x² + x¶).

Step-by-step explanation:

The set of all vectors in R² whose second component is the cube of the first can be described as all vectors of the form ℓ = (x, y) where y = x³.

To resolve this vector into components along the x and y axes, one would consider x to be the x-component and x³ to be the y-component. Since these components share a common axis, adding them follows the rule of ordinary number addition along their respective directions.

The magnitude R of any of these vectors can be found using the Pythagorean theorem as R = √(x² + y²) = √(x² + (x³)²), which simplifies to R = √(x² + x¶).