Final answer:
The statement is False because the vectors broken down into x and y directions are called component vectors, not resultants. The term 'resultant' refers to the vector obtained from combining two or more vectors. Breaking down a vector into its components is a common practice in physics to simplify calculations and understand the effects in each direction separately.
Step-by-step explanation:
True/False: A single vector can be replaced by two vectors in the x- and y-directions that are at right angles to each other. These two x and y vectors are not called the resultants of the original vector; rather, they are called the component vectors. The statement as given is False, because the term 'resultant' is used to describe a vector that results from the combination, or sum, of two or more vectors. On the contrary, the individual vectors in the x- and y-directions that represent the original vector are called components or component vectors. For example, using Cartesian coordinates, a vector α can be expressed as the sum of its x-component (αx) and y-component (αy).
A single vector can indeed form the shape of a right-angle triangle with its x and y components, confirming that the breakdown into components is valid. Moreover, knowing the magnitudes and directions of any two vectors that are not parallel, one can find the magnitude and direction of the resultant vector, which is the combined effect of the two vectors. Resolving vectors into their scalar components allows for the analytical use of vector algebra to perform operations such as addition, subtraction, and finding resultants.