1. Find the vector equation of a line in IR that passes through the points P(3, 6, 0) and Q(-2, 3, 1). O l(t) = (-5t, -3t, t) O l(t) = (-2 + 3t, 3 + 6t, 1) O e(t) = (-2+5t, 3 +3t, 1 -t) O e(t) = (-2t, 3t, t) O e(t) = (3 - 2t, 6 + 3t, t) 2. A ABC is a triangle in IR3 with vertices A(0, -2, 10), B(8, 8, 1), and C(-8, 8, 14) and mLA = 90. Find a parametric equation for the hypotenuse of A ABC. O h(t) = (-8t, -2 + 10t, 10 + 4t) 0 Sts1 O h(t) = (-8t, -2 + 10t, 10 - 9t) 0 Sts 1 O h(t) = (8 - 16t, 8, 1 + 13t) 0 St s1 O h(t) = (8 - 8t, 8 - 8t, 1 - t) Osts1 3. Find a vector equation for the line through the point (3, -1, 2) that is perpendicular to the plane 6x - 2y + 4z + 5 = 0. O e(t) = (3 +6t, -1 - 2t, 2 + 4t) O ((t) = (3 +3t, -1 - 3t, 2 + 2t) O l(t) = (6 + 3t, -2 - t, 4 + 2t) O e(t) = (6 + 3t, -2 - 3t, 4 + 2t) Find symmetric equations for the line through the point (-7, 12, 4) parallel to 3 i - 23 - 47. 7+x _12+y_4+z 3 2 O -3+2 -2- y y _ -4-z 12 O 3+2_ 2+y 4+ z 12 12 - y 4 - z 2 5. True or false? If L1 and L2 are two lines in Is which have no intersection, then L1 and L2 are parallel. True False 6. Let L1 and Ly be two lines in IRS with equations li (t) = (a1 + uit, Bi + vit, vi + wit) and l2(t) = (@2 + ugt, B2 + vat, 72 + wat), respectively. True or false? If L1 and L2 are perpendicular, then (u1, v1, w1) . (u2, v2, w2) = 0. True O False 7. AABC is a triangle in IRS with vertices A(0, -2, 10), B(8, 8, 1), and C(-8, 8, 14) and mLA = 90. Find a scalar equation for the plane containing A ABC. O 27: + 20y + 4z = 0 13x + 4y + 16z - 152 = 0 O -41x + 40y + 8z - 72 = 0 13x - 15y + 16z - 190 = 0 8. Find the equation of the plane which contains the line L1 described by , 1-y _z+3 - and the line L2 described by y -1 _-z-3 O -z - 3y + 2z + 11 = 0 O 3x + 9y + 5z + 20 = 0 5x + 14y + 16z + 34 = 0 O 4x - 2y + 32 + 17 = 0 9. Let 6 be the angle between the planes 5(x - 2) - 2v11(y + 1) + 10z = 0 and 2v11(x + 5) + 6(y - v11) - 8(z - 5) = 0. Find the exact value of cos 0. O cos 0 = -78 40 + V11 O 10 + V11 cos 0 = =40 - V11 78 O cos 0 = =10 - V11 V305 10. Find the distance from the point P(3, -2, 5) to the plane with normal vector 7 = (-4, 8, 9) which contains Q (1, 0, 2). Enter the exact value of the distance - do not round to a decimal. Preview will appear here... Enter math expression here1. Letg(I) = 3 - 5-2. Find the range of g(I). O (-00, 0) O (5,00) O (0, 00) O (3, 00) O (-00, 2) O (-00, 3) 2. What is the domain of f (x) 163 - 4' O (1/2, 00) O (-00, 00) O (2, 00) O (-00, 2) U (2, 00) O (-00, 1/2) U (1/2, 00) 3. Find the domain of y (x) = 5 + In(x - 2). O [0, 00) O [2, 00) O (0, 00) O (0, 2) O (2, 00) 4. Find the domain of y (T) = log(I) - 1 O (10, 00) O (0, 00) O (1/10, 00) O (-00, 00) O (0, 10) U (10, 00) O (0, 1/10) U (1/10, 00) 5. Leth(z) = 3 - 3. What is the I-intercept of h(I)? O (-3, 0) O (1, 0) O (0, 0) The graph has no I-intercept. O (3, 0) 6. Let f(z) = 3e2 + 1. Find the difference quotient, - f (z + h) - f(z) O 3elt (eh - 1) O 3e2z (1 - ezh) O 3ezh h 3ezz (ezh - 1) 7. Let f(z) = 3 In(x) - 2. Find an expression for f-1(I). Of 1(z) = e3(2+2) Of 1(z) = 32-2 Of-1(z) = 075-2 Of-1(z) = 3e -2 Of-1(z) =ey 8. Letg(x) = er+1. Find an expression for g-1(I). O g l(z) = In(z +1) O gl(z) = In(z) - 1 Ogi(z) = In(z - 1) Ogi(z) = In(z) +1 9. Use the logarithm rules to simplify the expression. eln(z)+2 In(y) O 2ry O zy2 O ezzy O ery 10. Solve for T. If necessary, enter your answer as a decimal rounded to the nearest tenth. Enter a number only for your answer (do not write x=). log2(2x) - 2 10g2(I - 1) = 2 Enter answer here1. Consider the function h(z) = - In (4 +1 Find the domain and range of h (select one answer for each). Domain (-00, 00) Domain (-1, 00) Domain (1 - e, 00) O Domain (-1, e - 1) U (e - 1, 00) Domain (1 - e, -1) U (-100) Range (-oo, 0) U (0, 00) Range (0, 00) Range (-00, 1) U (1, 00) Range (-1, 00) Range (0, 1) U (1, 00) 2. Find all intercepts of h(I) In (241) +1 O T-intercept: (1, 0) O T-intercept: (e - 1, 0) No I-intercept O y-intercept: (0, 1) O y-intercept: (0, -1) No y-intercept 3. Solve for I. log2(z + 5) + log2(I - 1) = 4 Enter answer here 4. Which of the trigonometric functions have domain (-00, oo)? Select all that apply. sec z O cot I O sin a O COS I O tan r 5. Use trigonometric identities to find the exact value of tan(-75). Preview will appear here. Enter math expression here 6. Find a solution T E (-7 /2, 7/2) for the following equation: (sec x + csc z) (sin a + cos z) = cota + 1 Write pi for 7. Preview will appear here... Enter math expression here 7. AABC is a triangle in IRS with vertices A(4 + v5, 3v5, 4), B(2v5, 2v/5, 2 - 2v/5), and C(v5, 2v/5, 2). Classify ABC as equilateral, isosceles, or scalene. Equilateral (all sides have equal length) Isosceles (two sides have equal length) Scalene (all sides have different lengths) 8. As before, let .ABC be the triangle with vertices A(4 + v5, 3v5, 4), B(2v5, 2v/5, 2 - 2v5), and C(v5, 2v/5, 2). Find the symmetric equations for the line on which side AB lies. O I - 2V/5 y - 2V/5 _z-2+2v5 4+ v5 3v/5 O x - 4+ v5 _y-V5 2 -2-2V5 2v/5 2V/5 2-2V/5 O z -4-v5_y-3v5 z -4 2V/5 2V/5 2 -2V/5 O x - 2v/5_y - 2V/5 z - 2+2v5 4-V5 V5 2+2v/5 9. As before, let A ABC be the triangle with vertices A(4 + v5, 3v5, 4), B(2v5, 2v5, 2 - 2v5), and C(v5, 2v5, 2). Classify ABC as acute, right, or obtuse. Acute (contains three acute angles) Right (contains a right angle) Obtuse (contains an obtuse angle) 10. As before, let A ABC be the triangle with vertices A(4 + v5, 3v5, 4), B(2v5, 2v5, 2 - 2v5), and C(v5, 2v5, 2). Find the scalar equation for the plane containing A ABC. O 4x + vay + 2z = 0 O -2: + 2vby - z - 16= 0 O -2z + 2v5y - z +4v/5=0 O -2x + 2v/5y - z - 18 + 2v/5=01. Evaluate cot () Do not write your answer as a decimal. If your answer includes a square root, write sqrt. For example v5 would be written sqrt(5). Preview will appear here... Enter math expression here 2. Find the exact value of cos (1050). O V2 - V6 O 2 - V3 O V3 + 2 O V6 - V2 O V6 + V2 3. Letg(x) = 4 cos(x) + 1. What is the range of g(I)? O [-3, 5] O [-5, 3] [0, 2] O [-4, 4] O [-1, 1] . What is the domain of tan ? All real numbers I except = = kn, k = 0, +1, 42,... All real numbers I except I 7 + kx, k = 0, +1, 42, ... All real numbers I All real numbers I except 2 + 2kx, k = 0, +1, 42, ... All real numbers I except: = 2kn, k = 0, +1, 42, ... 5. Letk(x) = 2 cos (Zz). What is the period of k(I)? Preview will appear here. Enter math expression here 6. Which of the following are odd functions? Select all that apply. ONone of these are odd functions. sec I O tanz CSC Z coS I cot z O sin a 7. Which of the following is equal to cos (2 - )? O COS I O - cos I O - sinc O sin a 8. Simplify the expression 3 cos? r + 2 sina. O cos? z + 2 0 3 None of these 0 2 O sin' z + 3 9. Find all t E [0, 27] such that 2 sin't + 7 cost = 5. Ot = O t = " or LIT Ot = T No solution Of = For 3 10. sec x + 2 tan a = 2. Find all solutions I E [0, TT). 6 OF=T T 27 3' 3 1 = ' 6 OI =1. Let u be the vector from the point (1, 7, 0) to the point (-4, 9, -3). Write v in terms of the standard basis vectors i , j , K. For example, the vector (-1, 2, -3) = (-1) . i + 2 . 3 + (-3) .