Question

An object is suspended from two cables that meet at a point above the object. One cable pulls with a force modeled by F1 = −78i + 44j. The other cable pulls with a force modeled by F2 = 87i + 80j. What is the angle between the cables? Round to the nearest degree.150°108°104°71°

Answer 1

From the information given, the forces are

F1 = −78i + 44j

F2 = 87i + 80j

We would apply the dot product.

F1F2 = <- 78, 44> * <87i, 80j>

F1F2 = - 78(87) + 44(80) = - 6786 + 3520

F1F2 = - 3266

|F1| = √[(- 78)^2 + 44^2] = √8020

|F2| = √[87^2 + 80^2] = √13969

The angle between them is

θ = Cos^-1[F1F2/(|F1||F2|)

θ = Cos^-1(- 3266/√8020 * √13969

θ = Cos^-1(- 0.30856)

θ = 108 degrees

the angle between the cables is 108 degrees