Final answer:
To find the sum of vectors A and B, calculate the components of each vector along the x- and y-axes using their magnitudes and directions. Sum the components to determine the resultant vector's components, and then calculate its magnitude and direction.
Step-by-step explanation:
When working with vector addition problems, the components of each vector along the x- and y-axes must be calculated based on the given magnitudes and angles. For vector A, with a magnitude of 122 cm and an angle of 145°, the components are found using trigonometric functions. The x-component is Ax = A * cos(θ), and the y-component is Ay = A * sin(θ). Similarly, for vector B, with a magnitude of 110 cm and an angle of 270°, Bx = B * cos(θ), and By = B * sin(θ). After calculating the components, the resultant vector's components are the sum of the individual x-components and y-components. The magnitude of the resultant vector R is then calculated using the Pythagorean theorem, |R| = √(Rx² + Ry²), and the direction is found by calculating the angle using the inverse tangent function, θ = atan(Ry/Rx).