A force is applied to an eye bolt as shown if f 10 kips

Question

Problem 1: Use the Law of Sines and the Law of Cosines to determine the magnitude of the resultant R and the angle θ between the x-axis and the line of action of the resultant.

Problem 2: A force is applied to an eye bolt as shown. If F = 10 kips, θ_x = 60°, θ_y = 70°, and θ_z, = 37.3°.

a. Determine the x-, y-, and z-components of the force.

b. Express the force in Cartesian vector form.

Problem 3: What is the unit vector in the direction of the force 2000i - 3000j + 6000k lb?

Problem 4: Two vectors U = 3i - 2j + 6k and V = 4i + 12j - 3k.

a. Determine the magnitude of U and V.

b. Determine the magnitude of the vector 3U + 2V.

Problem 5: Determine the magnitude R of the resultant and the angle θ_x between the line of action of the resultant and the x-axis for the three forces shown.

Problem 6: What is the dot product of the position vector r = 4i - 12j - 3k (ft) and the force F = 20i + 30j - 10k (lb)?

Problem 7: Find the dot product of the vectors M = - 0.2i + 0.4j + k lb and N = 0.1i + 0.8j -0.2k (ft).

Problem 8: Determine the x and y components of the 800 lb force.

Problem 9: Determine the magnitude and the coordinate direction angles (angles with each of the axes) of the result force acting at point A.

Problem 10: Given three vector, A = 2i- j + 4k,   B = 6i + 2j - k,   C= -4i + j

Determine the following vector products:

a. A x B

b. B x A

c. A x (B x C)

d. i x B

e. C x k