Final answer:
The statement is false; a 2-D vector is represented as the sum, not the product, of its x and y components, which are the orthogonal projections on the respective axes and when combined, form the original vector.
Step-by-step explanation:
The statement that every 2-D vector can be expressed as the product of its x and y-components is false. In reality, a two-dimensional (2-D) vector can be expressed as the sum of its x and y components. When we talk about a vector in the context of a Cartesian coordinate system, we represent it as a directed line segment with both direction and magnitude. The vector can be broken down into two parts: one along the x-axis, known as the x-component, and one along the y-axis, known as the y-component.
The x and y components of a vector are essentially the orthogonal projections of the vector onto the respective axes. When you add these components together, using vector addition rules, they give you the original vector. It is important to note that the Pythagorean Theorem can be used to find the magnitude of the resultant vector when the x and y components are perpendicular to each other, forming a right angle triangle.