Final answer:
The question is about vector addition in two dimensions, requiring the resolution of given vectors into their x and y components and calculating the sum of the components to determine the resultant vector's magnitude and direction.
Step-by-step explanation:
The question involves calculating the result of vector addition in two dimensions, specifically finding the sum of vectors A and B. The given vectors are A = (122 cm, < 145°) and B = (110 cm, < 270°), and the task is to calculate A + B.
This process involves resolving both vectors into their x and y components using trigonometry and then adding these components together to find the resulting vector.
To solve for the x and y components, we use the formulas:
Ax = A cos θ
Ay = A sin θ
Bx = B cos β
By = B sin β
After finding the components, we sum the x-components and the y-components separately:
Resultant x-component (Rx) = Ax + Bx
Resultant y-component (Ry) = Ay + By
Finally, to find the magnitude and direction of the resultant vector, we calculate:
Magnitude = √(Rx² + Ry²)
Direction θ = arctan(Ry / Rx)
In this example, without the numerical calculations, the formula suggests one of the choices provided in the question would be the correct answer for the magnitude and direction of the resulting vector after performing these operations.