1. Given the vectors PP and QQ shown on the grid, sketch and calculate the magnitudes of the vectors (a)M=P+QM=P+Q and (b)K=2PQK=2P-Q. Use the tail-to-head method and express the magnitudes in centimeters with the aid of the grid shown in the drawing.

2. Vectorhas a magnitude of11.2units and points due west. Vectorpoints due north.(a)What is the magnitude ofif+has a magnitude of18.2units?(b)What is the direction of+relative to due west?(c)what is the magnitude ofif-has a magnitude of18.2units?(d)What is the direction of-relative to due west?

(Note: Use the convention that an angle north of west is positive, and an angle south of west is negative.)

3. A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the 30.0 angle. The magnitude of the force applied by each rope is 2900 newtons (N). (a) How much force would a single rope need to apply to accomplish the same effect as the two forces added together? (b) What angle would the single rope make relative to the dashed line?

4. A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the 30.0 angle. The magnitude of the force applied by each rope is 2900 newtons (N). (a) How much force would a single rope need to apply to accomplish the same effect as the two forces added together? (b) What angle would the single rope make relative to the dashed line?

5. The components of vector AA are A_x and A_y (both positive), and the angle that it makes with respect to the positive x axis is . Find the angle if the components of the displacement vector AA are (a)A_x = 12 m and A_y = 12 m, (b)A_x = 18 m and A_y = 12 m, and (c)A_x = 12 m and A_y = 18 m.