Question

Lines AB and CD are parallel. Find the measures of angle AFB 1570 C 42° F B

Answer 1

To find the sum of two vectors given in polar form, convert the vectors to their rectangular components, add these together, and then convert back to polar form to get the overall magnitude and direction of the resulting vector.

Step-by-step explanation:

The question involves the addition of two vectors represented in polar form. To find the sum of the vectors A + B, we need to convert them into their rectangular components and then add these components together. Here are the steps to find the components and the resulting vector:

1. Determine the x and y components of each vector using trigonometry: Ax = A cos θ and Ay = A sin θ, where θ is the angle in degrees.
2. Once you have the components, add the corresponding x components and y components: Rx = Ax + Bx and Ry = Ay + By.
3. Convert the resultant vector back to polar form to find the magnitude and the angle.

For instance, if we were given vectors A and B as A = (53.0 m, < 20.0°) and B = (34.0 m, < 63.0°), we would first find their x and y components before adding them together to find A + B.

Answer 2

The sum of vectors A and B, with given magnitudes and directions, is found by breaking each into components, summing these components, and using trigonometry to find the resultant vector's magnitude and direction. The correct sum is 232 cm at an angle of 201.8°.

Step-by-step explanation:

To find the sum of the vectors A and B, we must first determine their components in the x- and y-axes. The vector A has a magnitude of 122 cm and a direction at an angle of 145°, while vector B has a magnitude of 110 cm and is directed at an angle of 270°. To break these vectors into components, we use the cosine and sine functions for the x and y components, respectively.

For vector A, the x-component (Ax) is calculated by A cos θ, and the y-component (Ay) by A sin θ. Similarly, we calculate B's components using its magnitude and direction. In this case, since B's angle is 270°, it has no x-component (Bx = 0) and a negative y-component due to the sine of 270° being -1.

Once we have these components, we sum them to find the resultant vector's x and y components. The magnitude of the resultant vector is then calculated using the Pythagorean theorem, and its angle is found using the arctangent function of the y-component over the x-component. From the provided options, we can deduce that option d, 232 cm, θ = 201.8°, is the sum of the vectors A and B given their described components and angles.