Calculus 3 :

Section 10.6: Problem 1 (1 point) Match the surfaces with the appropriate descriptions. 1.2=1-212 2. 2 = 212 + 372 3. 2=4 4. I' + 273 + 323 = 1 5. 2=12 6.1ty =5 7. 2 = 21 + 3y A. hyperbolic paraboloid B. parabolic cylinder C. elliptic paraboloid D. horizontal plane E. ellipsoid F. nonhorizontal plane G. circular cylinderSection 10.3: Problem 15 (1 point) Consider the vectors a = 3it j - k, b= 1-3j+k, c=1-3j d =31- jok, g= -31-j+k. Which pairs (if any) of these vectors are (a) Are perpendicular? (a,c) (09) (Enter none or a pair or list of pairs, e.g., if d is perpendicular to b and c, enter (a, b), (a,c).) (b) Are parallel? (ag) (Enter none or a pair or list of pairs, e.g., if d is parallel to b and c, enter (a, b), (a,c).) (c) Have an angles less than /2 between them? (a,d). (b,d). (6,2), (c,d) (Enter none or a pair or list of pairs, e.g., if d is at an angle less than pi/2 from b and c, enter (a, b), (a,c).) (d) Have an angle of more than w/2 between them? (a,b).((ac),(dg)) (Enter none or a pair or list of pairs, e.g., if d is at an angle greater than pi/2 from b and d, enter (a, b), (a,c).)Section 10.5: Problem 10 (1 point) ATTEMPT NOT ACCEPTED -- Please submit answers again (or request new version if necessary). Determine whether the lines L1 : I= 23 + 6t, y = 5 +t, 2=t and L2 : I = 947t y= -4+3t = =-11 +4t intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty. Do/are the lines: intersect v Point of intersection: ( -24 -24 -24Section 10.5: Problem 19 (1 point) Find an equation of the plane consisting of all points that are equidistant from A(0, 3, 3) and B(-3, -3, -3). 3x + 47 + 47 + 3 =0 Note: you have to enter the full equation.Section 10.5: Problem 21 (1 point) Consider the planes 3x + 1y + 2: = 1 and 32 + 2z =0. (A) Find the unique point ]' on the y-axis which is on both planes. (B) Find a unit vector u with positive first coordinate that is parallel to both planes. 11 k (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes. r(t) kSection 10.6: Problem 2 (1 point) Match the equation with its graph labeled A-F. You may click on any image to get a larger view. A. B. D. E. F. 1. x' 4 223 = 1 2. 13 - 13 + 23 = 1 3. I' + 47 + 923 = 1 4. 12 = 13 4 2:2 5. y = 13 - 22 6. 9r' + 4y- + 23 = 1Section 10.6: Problem 3 (1 point) State the type of the quadratic surface: (E) + (1 )3 + (8) = 1 1. Ellipsoid 2. Hyperboloid of one sheet 3. Hyperboloid of two sheets 4. None of these Describe the trace obtained by intersecting with the plane = = 1: 1. Ellipse 2. Hyperbola 3. Circle 4. Empty setSection 10.6: Problem 4 (1 point) (4) Match the ellipsoids shown in the figure above with the equations: 1) 1' + 4y' + 423 = 16 2) 413 + y3 + 423 = 16 3) 47 + 4y' + 23 = 16Section 10.6: Problem 5 (1 point) State whether the equation + (4 2 defines: A hyperbolic paraboloid Previev An elliptic paraboloid An elliptic cone You have None of these You have 2 attempts remaining.Section 10.6: Problem 6 (1 point) State whether the equation 91' - 473 - 4023 = 1 defines (enter number of statement): 1. A hyperboloid of two sheets 2. A hyperboloid of one sheet 3. An ellipsoid 4. None of theseSection 10.6: Problem 7 (1 point) Find the equation of the ellipsoid passing through the points ( 15, 0, 0), (0, 14, 0) and (0, 0, 17)Section 10.6: Problem 8 (1 point) State the type of the quadratic surface: 12 - (#)' + 23 =1 1. Hyperboloid of two sheets 2. Hyperboloid of one sheet 3. Ellipsoid 4. None of these Describe the trace obtained by intersecting with the plane y = 0: 1. Ellipse 2. Hyperbola 3. Circle 4. Empty setSection 10.3: Problem 14 (1 point) ATTEMPT NOT ACCEPTED -- Please submit answers again (or request new version if necessary). The force on an object is P = -24 j. For the vector D = -3 i - 5 j, find: (a) The component of F parallel to : 180 108 17 i 17 (b) The component of F perpendicular to u: The work, W, done by force F through displacement v: 120