Question

Part A: /2 (trig form vectors) /2 (work shown)

Part B: 1 (dot product) /2 (work shown)
Part C: 1 (Angle between cable)/2 (work shown)
An object is suspended by two cables attached at a single point. The force applied on one cable has a magnitude of 150 pounds and acts at an angle of 55: The force on the other cable is 80 pounds at an angle of 170"
Part A: Write each vector in component form Show all necessary work
Part B: Find the dot product of the vectors Show all necessary calculations
Part C: Use the dot product to find the angle between the cables, Round the answer to the nearest degree. Show all necessary caculations

Answer 1

To complete the given questions, we need to write the vectors in component form in Part A, find the dot product of the vectors in Part B, and use the dot product to find the angle between the cables in Part C.

Step-by-step explanation:

In order to complete Part A, we need to write each vector in component form. For the first vector, which has a magnitude of 150 pounds and an angle of 55 degrees, the x-component can be found using the formula Ax = A * cos(theta), where A is the magnitude and theta is the angle. Similarly, the y-component can be found using Ay = A * sin(theta). For the second vector, with a magnitude of 80 pounds and an angle of 170 degrees, we can use the same formulas to find the x and y components.

For Part B, we can find the dot product of the two vectors by multiplying their corresponding components and adding up the results. The dot product is given by the formula A · B = Ax * Bx + Ay * By.

For Part C, we can use the dot product to find the angle between the cables. The angle can be found using the formula cos(theta) = (A · B) / (|A| * |B|), where theta is the angle between the cables and |A| and |B| are the magnitudes of the vectors