1. Fill in the blanks. Consider the following vector v from (0, 0) to (a,b). v = ai + bj The horizontal component of v is The vertical component of v is _ The magnitude of v is given by | vl| =_ The horizontal component of v is (1) The vertical component of v is (2) The magnitude of v is given by |v| = (3). (1) O b. (2) O a. (3) O vatb. O a. O b. O V(ai)2 + (bj)2 O ai. Obj. O Va2 + 62 bj. O ai O vai + bj . 2. Complete the sentence below. If v = (a,b) is an algebraic vector whose initial point is the origin, then v is called a(n) vector. A vector whose initial point is the origin, then v is called a(n) (1) vector. (1) O force O unit O position O velocity O nonzero3. Fill in the blanks. Vector v with initial point P1 2 (X131) and terminal point P2 = (x2312) is equal to the following vector. V = (_li + (H Vector v with initial point P1 2 (X131) and terminal point P2 = (x2312) is equal to the following vector. vztlt} )i+(t2} )i (1) O V2'Y1 (2) 0 X2 *1 O Y1'Y2 0 X1 X2 0 X1'X2 O Eta3'1 0 X2 X1 0 Y1 3"2 4. Fill in the blanks. Let v be a nonzero vector. If B is the direction angle measured from the positive x-axis to v. then the vector can be expressed in terms of its magnitude and direction angle as follows. v = IIVIl_i + \"VIIi Let v be a nonzero vector. If Iii is the direction angle measured from the positive x-axis to v. then the vector can be expressed in terms of its magnitude and direction angle as follows. v: \"v" ('1) i + \"v\" (Zrj (1) 0 cost} (2) O tank) 0 tank) O sint-J O sint-J O cost} 5. Complete the sentence below. If F, and F, are two forces simultaneously acting on an object, the vector sum F, + F, is called the force. If F, and F, are two forces simultaneously acting on an object, the vector sum F, + F2 is called the (1) force. (1) O effective O resulting O resultant O sum 6. Let v be the vector from initial point P, = (-2, -9) to terminal point P2 = (7,4). Write v in terms of i and j. The vector from point P, = ( -2, -9) to point P2 = (7,4) is v = (Simplify your answer. Type your answer in terms of i and j.) 7. Let u = 9i - 5j and v = - 10i + 8j. Find the vector u + v. u + v= (Simplify your answer. Type your answer in terms of i and j.) 8. Let u=2i - 6j, and v = - 5i + 7j. Find u - v. u - V = (Type your answer in terms of i and j.) 9. Let v= - 6i + 5j, and w = - i -7j. Find 2w + 5v. 2w + 5v = (Type your answer in terms of i and j.) 10. Let v= - 8i + 6j and w = - i - 6j. Find 2v - 7w. 2v- 7w= (Simplify your answer. Type your answer in terms of i and j.) 11. Let u = 4i - 2j, and w = - i -6j. Find |w - ull. 1/ w - ull = _ (Type an exact answer, using radicals as needed.)12. Find the unit vector that has the same direction as the vector v. v = 10i + 24j The unit vector that has the same direction as the vector v is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in terms of i and j. Rationalize all denominators.) 13. Find the unit vector that has the same direction as the vector v. v = 13i - 5j The unit vector that has the same direction as the vector v = 13i - 5j is (Simplify your answer, including any radicals. Type your answer in the form ai + bj. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) 14. Write the vector v in terms of i and j whose magnitude | v | and direction angle 0 are given. 1/V/1 = 6, 0=60 V = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Type your answer in the form ai + bj. Rationalize all denominators) 15. Write the vector v in terms of i and j whose magnitude and direction angle are given. |v/ = 7, 0=113 V= (Type your answer in terms of i and j. Round to the nearest hundredth as needed.) 16. Let u= - 4i + 5j, v=2i - j, and w = - 7i. Find 4u - (2v - w). 4u - (2v -W) = (Type your answer in terms of i and j.) 17. Let u = - 7i + 8j and v = 2i -j. Find lu + v/|2 -|ju -v/|2. llu + v/12 - 1/4- v/12 =118. Find the magnitude |v|| and the direction angle 0 for the given vector v. v = - 9i + 11j (Round to the nearest hundredth as needed.) =0 (Round to the nearest tenth as needed.) 19. The forces F1, F2, F3. ..., F acting on an object are in equilibrium if the resultant force is the zero vector. F1 + F2 + Fg + ... + Fn =0 The forces F, = 8i - 8j and F2 = 6i + 2j are acting on an object. a. Find the resultant force. b. What additional force is required for the given forces to be in equilibrium? a. The resultant force is (Simplify your answer. Type your answer in terms of i and j.) b. The additional force required for the given forces to be in equilibrium is (Simplify your answer. Type your answer in terms of i and j.) 20. The figure shows a box being pulled up a ramp inclined at 12 from the horizontal. Use the following information to solve the problem. 120 -120 BA = force of gravity, |BA = weight of the box IACI = - magnitude of the force needed to pull the box up the ramp BC = magnitude of the force of the box against the ramp If a force of 20 pounds is needed to pull the box up the ramp, find the weight of the box. The weight of the box is approximately pounds (Type an integer or decimal rounded to the nearest tenth as needed.)