Final answer:
The question involves using trigonometric functions to find the components of vectors A and B along the x- and y-axes. By applying formulas for the x-components and y-components, we can solve problems pertaining to vector addition, subtraction, and finding the magnitude and direction of resultant vectors.
Step-by-step explanation:
The question seems to involve finding the components of vectors A and B along the x- and y-axes, given the magnitudes of the vectors and angles with respect to a reference direction. To find the components, we use the formulae: Ax = A × cos(θ) for the x-component, and Ay = A × sin(θ) for the y-component, where θ is the angle the vector makes with the positive x-axis. These components are essential as they allow for vector addition, subtraction, and finding the resultant vector in Cartesian coordinates.
For example, if A = 53.0 m and the angle 0A = 20.0° while B = 34.0 m and angle B = 63.0°, we would find Ax and Bx for the x-components. Subsequently, for the y-components, we would use Ay and By. The proper application of trigonometric functions like cosine and sine to their respective angles would yield the result for each component.