1. Vector A^→ has y-component A_y = +9.60 m. A^→ makes an angle of 32.0° counterclockwise from the +y-axis.

(a) What is the x-component of A^→?

(b) What is the magnitude of A^→?

2. Vector A^→ is in the direction 34.0^° clockwise from the -y-axis. The x-component of A^→ is A_x = -16.0 m.

(a) What is the i-component of A^→?

(b) What is the magnitude of A^→?

3. Find the magnitude and direction of the vector represented by the following pairs of components:

(a) A_x = -8.60 cm, A_y= 5.20 cm;
(b) A_x = -9.70 m, A_y = -2.45 m;
(c) A_x = 7.75 km, A_y = -2.70 km.

4. Vector A^→ is 2.80 cm longg and is 60.0^° above the z-axis in the first quadrant. Vector B^→ is 1.90 cm long and is 60.0^o below the x-axis in the fourth quadrant (Fig. 1). Use components to find the magnitide and direction of

(a) A^→ + B^→;
(b) A^→ - B^→
(c) B^→ - A^→.

In each case sketch the vector addition subtraction and show that you aamerical answers are in qualitative agreement with your sketch.

5. (a) Write each vector in Fig. 2 in terms of the unit vectors i^ and j^.

(b) Use unit vectors to express vector C^→, where C^→ = 3.00A^→ - 4.00B^→.
(c) Find the magnitude and direction of C^→.

6. You arc given two vectors A^→ = -3.00i^ + 6.00j^ and B^→ = 7.00i^ + 2.00j^. Let counterclockwise angles be positive.

(a) What angle does A^→ make with the +x-axis?
(b) What angle does B^→ make with the +x-axis?
(c) Vector C is the sum of A^→ and B^→, so C^→ = A^→ + B^→. What angle does C^→ make with the +x-axis?

7. Two ropes in a vertical plane cult equal-magnitude forces on a hanging weight but pull with an angle of 72.0° between them. What pull does each rope exert if their resultant pull is 372 N directly upward?

8.  Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A^→, B^→, and C^→ shown in Fig. 3. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero.

9. Dislocated Shoulder. A patient with a dislocated shoulder is into a traction apparatus as shown in Fig. 4. The pulls A^→ and B^→ have equal magnitudes and must combine to produce an outward traction force of 12.8 N on the patient's arm. Bow large should these pulls be?

10. Vectors A^→ and B^→ have scalar product -6.00, and their vector product has magnitude +9.00. What is the angle between these two vectors?

11. Vector A^→ has magnitude 12.0 m, and vector B^→ has magnitude 16.0 m. The scalar product A^→ • B^→ is 112.0 m². What is the magnitude of the vector product between these two vectors?

12. The scalar product of vectors A^→ and B^→ is +48.0 m². Vector A^→ has magnitude 9.00 m and direction 28.0° west of south. If vector II has direction 39.0° south of east, what is the magnitude of B^→?