13. Find the torque produced by a cyclist exerting a force of F = [45, 90, 130]N on the shaft- pedal d = [12, 17, 14] cm long. a) (-950, 930, -315) b) 3890 c) 19874 d) 1866625 14. Given a = [3, -1, 4]& c = [-2, 6, t], find t so that a and c are perpendicular. 1) 4 b) -3 C) -4 d) 3 15. Given u = [-12, 6, k]& v = [4, -2, 4], find k so that u and u are parallel. a) 4 b) - 3 ) 6 d) -12 16. An object moves along a straight line in such a way that its position is s(t) = -5t3 + 17t2, in which t represents the time in seconds. What is the object's acceleration at 2.7 seconds? a) -47 b) -17.55 c) 17 d) -81 17. Find the unit vector of a = [-3, -7, 4]. a) = [-3, -7, 4] b ) [ - 3 , - 7 , 4 ] C) (VIA' VIA' VI. d) VTA' VTA' V74 18. Derive y = -2(3-7x) a) -2In3(3-7x) b) -14In7(3-7x) c) 7ln2(3-7x) d) 143(3-7x) Thinking [27 Marks] 19. Given: f (x) = -2x+1 , f'(x) = *+8x-9 50 x+4 (x+4)2 & f "( x ) = (x+4)3, determine (if applicable): i) The equation(s) of the vertical, horizontal and/or slant asymptotes. Don't forget the behaviours of the graph near the asymptotes. [4 Marks] ii) The x and y intercepts [2 Marks]13. Find the torque produced by a cyclist exerting a force of F = [45, 90, 130]N on the shaft- pedal d = [12, 17, 14] cm long. a) (-950, 930, -315) b) 3890 c) 19874 d) 1866625 14. Given a = [3, -1, 4]& c = [-2, 6, t], find t so that a and c are perpendicular. 1) 4 b) -3 C) -4 d) 3 15. Given u = [-12, 6, k]& v = [4, -2, 4], find k so that u and u are parallel. a) 4 b) - 3 ) 6 d) -12 16. An object moves along a straight line in such a way that its position is s(t) = -5t3 + 17t2, in which t represents the time in seconds. What is the object's acceleration at 2.7 seconds? a) -47 b) -17.55 c) 17 d) -81 17. Find the unit vector of a = [-3, -7, 4]. a) = [-3, -7, 4] b ) [ - 3 , - 7 , 4 ] C) (VIA' VIA' VI. d) VTA' VTA' V74 18. Derive y = -2(3-7x) a) -2In3(3-7x) b) -14In7(3-7x) c) 7ln2(3-7x) d) 143(3-7x) Thinking [27 Marks] 19. Given: f (x) = -2x+1 , f'(x) = *+8x-9 50 x+4 (x+4)2 & f "( x ) = (x+4)3, determine (if applicable): i) The equation(s) of the vertical, horizontal and/or slant asymptotes. Don't forget the behaviours of the graph near the asymptotes. [4 Marks] ii) The x and y intercepts [2 Marks]Knowledge/Understanding Multiple Choice: [18 Marks] 1. Determine a . b given thata = (2, -7) and b = (-3, 6) a) -36 b) -48 C) 48 d) 36 2. 3(2u - 30) - 2(5 - 5u) -4v simplified is: a) 16u - 150 b) 4u - 30 c) -3u - 67 d) 16u - 110 3. The function whose graph has a slant (oblique) asymptote is: 6x2 a) y= - x4 -2 x3+5x by = x4 -8x+9 x4+5 c) y = - x3+x2-1 d) b and c 4. The derivative of y = sin(7x - 4) is: a) 7cos(7x - 4) b) -7cos(7x - 4) c) cos(7x - 4) d) (7x - 4)cos(7x - 4) 5. The conjugate of 2V7 - V3 is: a) V3 - 2V7 b) - 2V7 + V3 c ) V7 + V3 d) 2V7 + V3 6. In R', the standard basis (unit) vector, k can be expressed in component form as: a) (1, 0, 0) b) (0, 1, 0) c) (0, 0, 1) d) (1, 1, 1) 7. Evaluate the following limits: lim v4 + v25 + x X-0 a) 2 + v5 b ) 3 c) +3 d) 7 8. The incorrect vector property is: a) at b = bta bax b = bxa c) a . b = b . a d) a - b = -bta 9. If a vector is described as an airplane flying North at 400km/h, then the opposite vector can be described as: a) An airplane flying North at -400km/h b) An airplane flying South at 400km/h c) An airplane flying South at 800km/h d) Both b and c 10. For u and v, if the sign of u . v is negative, then the angle between the tail to tail vectors will be: a) 0