Given the vectors, A and B, find A-B following the rules of vector addition.

Given vectors M and N in the figure below, which of the following is most likely the correct diagram for the vector difference M - N?

To describe a vector, we need both its magnitude and its direction. Determine the magnitude and direction of the resultant vector C when C = A + B using the graphical method (geometry and trigonometry).

A car has a position vector of 3.0 m with a direction of 45° clockwise from the north. Determine the components of the position vector along the x and y axes in the normal and tilted coordinate systems shown below.

A mountain climber of weight 637 N uses a fixed rope to ascend the inclined part of an artificial wall. The wall forms a right triangle structure. The wall's summit is 35.0 m above the ground and its base of 4.30 m is in contact with the ground. Calculate the magnitude of the climber's weight projection along the directions parallel and perpendicular to the inclined part of the wall.

Consider a velocity vector in the xy-plane with a magnitude of 12 m/s. The x-component of the vector's velocity is -7.0 m/s. i) Find the two possible values for its y-component. ii) Assuming the y-component velocity is confirmed as positive, identify the extra velocity vector needed to alter the vector's direction to be along the positive y-axis and a magnitude of 20 m/s.

A physics instructor directs three students to pull a ring, as shown in the image. The students have different abilities, hence exerting different pulls. One student applies 4.0 N on the first cable, and a second student exerts 6.0 N on the second cable. Determine the pull a third student must apply on the third cable to keep the ring stationary. Express the direction as an angle measured from the negative x-axis.

A circular driveway has a diameter of 10.0 m. A child circles the driveway at a constant speed. Use an x-y coordinate system whose origin is located at the center of the driveway; the +x-axis points to the east, and +y-axis points to the north. The child has an initial position (x,y) = (-3 m,4 m) and walks in a counterclockwise direction around the driveway. After 1.75 turns, determine the child's displacement vector. Express the result using magnitude and direction.

Work out the vector magnitude and direction of s = (12i + 9j) m/s. Draw the vector and mark the magnitude and direction.