Final answer:
To find the resultant vector of A + B, we calculate the components along x- and y-axes for each vector, sum these components, and then find the magnitude and angle using the Pythagorean theorem and trigonometry, respectively. The resultant has a magnitude of 232 cm at an angle of 201.8°.
Step-by-step explanation:
To find the resultant vector m∠A + m∠B of two given vectors, we can use the analytical method of vector addition. For vectors A = (122 cm, < 145°) and B = (110 cm, < 270°), we first need to break each vector down into its horizontal (x-axis) and vertical (y-axis) components using the cosine and sine functions for their respective angles.
The components of vector A on the x- and y-axes are Ax = A cos(∠A) and Ay = A sin(∠A). Similarly, the components of vector B on the x- and y-axes are Bx = B cos(∠B) and By = B sin(∠B).
After calculating these components, we sum the x-components and y-components separately to get the resultant vector's x and y components. Then, using Pythagorean theorem, we calculate the magnitude of the resultant vector, which brings us to the answer:
Magnitude: 232 cm, Angle: ∠ = 201.8°