Final answer:
A vector can indeed form the shape of a right angle triangle with its x and y components, which is true. However, a 2-D vector is not expressed as the product of its x and y components but as their vector addition.
Step-by-step explanation:
A vector can form the shape of a right angle triangle with its x and y components.
When we refer to the x and y components of a vector, we are talking about the projection of that vector along the x-axis and the y-axis, respectively. These components can be visualized as the legs of a right triangle, with the vector itself representing the hypotenuse. This is due to the fact that the x and y components are perpendicular to each other, satisfying the definition of a right angle. The concept is a fundamental aspect of vector representation in two-dimensional space. The x component can be found using the cosine of the angle between the vector and the x-axis, while the y component can be found using the sine of the angle.
For the second statement: Every 2-D vector can be expressed as the product of its x and y-components. This statement is not quite accurate. Every 2-D vector can be resolved or decomposed into its x and y-components, but the term product implies multiplication, which is not the case for vector components. Instead, vector components are combined through vector addition to form the resultant vector.