Determine the unit vectors along ca and cb in the cartesian

Question

Question 1. If the magnitude of the resultant force is to be 9 kN directed along the positive x-axis,

1. Draw the force-diagram, showing approximate magnitude and direction of the forces (including the resultant) and the parallelogram, with proper labels. (suggest use 1 cm ≡ 1 kN for clear picture)

2. Determine magnitude and direction (counterclockwise from positive x-axis) of the force T -using direct measurements - graphical method
(ruler & compass).

3. Confirm your answer analytically, using laws of sines and cosines.

Question 2. Rods AC and BC are attached to the vertical wall (AB), as shown, with smooth rings at A, B and C. The structure supports a horizontal load of magnitude 400 lbs. The distance between points A and B is 14 feet. The lengths of rods BC and CA are 13 feet and 15 feet, respectively.

Neglect the size of the rings.

Assuming the horizontal direction to be the x-direction and the vertical direction to be the y-direction:

Determine the unit vectors along CA and CB in the Cartesian co-ordinate system.

Question 3. If the magnitude for the resultant force acting on the plate is required to be 6 kN and its (the resultant) direction measured clockwise from the positive x-axis is θ = 30^o, determine the magnitude of F₂ and its unit vector.