An antelope is being pulled by two forces whose vector-component expressions are: F1 = 0Ni + -5.3Nj + 4.3Nk F2 = 4.6Ni + -0.3Nj + -5.1Nk What is the angle (in degrees) between these two vectors?

19. Two ropes are attached to a tree, and forces of F₁ = 2.01 +4.0Ĵ N and F₂ = 3.01 + 6.0ĵ N are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.

Question Four forces (measured in Newtons) act on a crate. The forces are given by the vectors: F₁ = 212i-136j + 241k N, F₂ = = 108i + 144j+ 189k N. F₂ = -400 + 180j + 240k N, and F₂ = -270€ N a) What is the resultant, R = F₁+F₂ + F3 + F4, of the four forces? What is the magnitude of the resultant force? b) If the displacement of the crate is given by d = 0.5i - 0.1j + 2.7k m What is the contribution by the first force F₁ to the work done, i.e. W = F₁. d? c) If the third force, F3, acts at the point (0.5, 0.8,0.1) m, what is the moment, M = r X F3, at the point (-0.5,0.8,0.7) m? d) What is the angle (in degrees to 2 decimal places) between the force vectors F₂ and F3? e) What is the force vector, F, that acts in the opposite direction to the force F₂ and has magnitude of 203 Newtons?

Problem 6: Consider the two vectors, A = -4.93 î+-2.99 Ĵ and B = -1.2 î+ -4.07. ) What is the magnitude of Ď= A - B?