1. Vector A→ has y-component Ay = +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 Ax = -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) Ax = -8.60 cm, Ay= 5.20 cm;
(b) Ax = -9.70 m, Ay = -2.45 m;
(c) Ax = 7.75 km, Ay = -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 60.0o 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→?