15} Given \"51' = 85 N and Izl = 125 N and they are acting at an angle of 140 to each other... a) Find the magnitude of the resultant. b] Describe the direction of P, + F2 relative to F1 16} A 120 N sign is hanging from two chains attached to a ceiling as shown. 3] Draw the vector diagram that illustrates this situation. 70.. 3 on b] Determine the magnitude of the tensions in the chains. 171A sign weighing 98 N is suspended from the middle of a 4 m long chain. The ends of the chain are attached to a ceiling at points 3 m apart. Determine the tensions in the chains. 18) A community center plans to install a new basketball hoop on the side of the building. The hoop and backboard have a combined weight of 196 N and are supported by a brace and a wire. Determine the magnitude of the tensions in the _, wire and the brace. 23) A truck weighing 17 000 N is resting on a ramp that is inclined at an angle of 15' to the horizontal. Resolve the weight of the truck into the rectangular components keeping it at rest. 25} Suppose forces of 45H and NM act at an angle of 110' to each other. Find the magnitude {to 1 decimal place) and direction (to the nearest degree} of the resultant force. State the direction as an angle off the MN force. 28} Determine the magnitude of the horizontal and vertical vector components of a 300 N force acting at an angle of 33 to the horizontal. 30} Express each vector in terms of vectors f and j' a) [3l _6] b) [01 _8] C) [6l0] 31) Express each vector in the form [a, b] a) 42 b) 7t 4}\" c] 2; 32} Write the coordinates of each Cartesian Vector in the form [(1, b] and determine its magnitude. 48} Find the magnitude of the projection of a on 3 and also the vector projection of (I on 3 if a = [6, 1] and E = [11.5] 38] A person pushes a lawnmower with a force of 250 N. The handle makes an angle of 35" with the ground. Write this force in component form as a Cartesian vector. 37! A person pulls a sleigh, exerting a force of 180 N along a rope that makes an angle of 30 to the horizontal. Write this force in component form as a Cartesian vector. 49) A superhero pulls herself 15 m up the side of a wall with a with a force of 500 N, at an angle of 12 to the vertical. What is the work done? 52) Determine its exact magnitude. 57) Determine the angle between the vectors 9' = [6,1,2] and H = [-53.6] 59) Identify the type oftriangle with vertices A(2,3, -5), B(4,8,1), and C (6, 4,D)