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Q1:Find the outward flux of the given vector field F on the region D which is bounded by the pparaboloid z = x² + y², and the plane z = 2y. F = 3x²y²i+yj - 6zxy²k Use the following trigonometric identities: cos² (t) = = X Z 1+cos (2t) 2 sin² (t)= = (20 pt.) 1-cos (2t) 2 z²+(y-1)² = 1 Projected area on x-y planeSee Answer
Q2:For each of the following scalar fields, find V²V (a) V₁ = x³ + y³ +2³ (b) V₂ = pz² sin 26 (c) V₁ = r²(1 + cos sin )See Answer
Q3:3.4 Find the length of a path from P₁(4, 0°, 0) to P₂(4, 30°, 0).See Answer
Q4:2.31 Describe the intersection of the following surfaces: (a) x = 2, y = 5 (b) x = 2, y = -1, z = 10 (c) r= 10, 0 = 30°See Answer
Q5:1.4 Let vectors A = 10a, (c) 2A - 3B. - 6a, + 8a, and B = a + 2a. Find: (a) A B, (b) A X B, .See Answer
Q6:10. Find the volume of the parallelepiped defined by the vectors u = [8, -3, 4], v = [-2, 9, 1], and w = [0,-1,7]. [4 marks] WSee Answer
Q7:7. Given a = [2, -10] and b = [-8, 23], find: a. 3a 2b [2 marks] b. ab [1 marks] c. a + b [2 marks] d. proj a [3 marks] e. The angle between a and b [2 marks]See Answer
Q8:6. Determine the vertical and horizontal components of each vector. [6 marks] a. 810 N at an incline of 15° from horizontal b. 80 m/s, 60° clockwise from verticalSee Answer
Q9:5. Use geometric addition of vectors to find the resultant of each combination. a. 18 km/h north and 16 km/h east. [2 marks] b. 12 N on a bearing of 25° and 17 N on a bearing of 100°. [4 marks]See Answer
Q10:Problem 4. (6+ 4 points) (i) Use Gauss-Jordan elimination to compute the inverse and determinant of the following matrix. B 2 -1 0 0 -1 0 0 2 -1 0 2 -1 -1 0 -1 2 (ii) Suppose that A is a 4 x 4 matrix such that adj(A) = B, i.e. the matrix in the previous part of the question. Find A. Hint: You may need to use certain mathematical statements stated in tutorial problem set 4. (In fact, this demonstrates that knowing the adjoint matrix of an invertible matrix allows you to recover the original matrix back.)See Answer
Q11:3. [4 points] Let X be a vector field on Rm such that for every p = Rm the maximal integral curve of X going through p at time zero is defined on the whole of R. Consider the stereographic projection : Sm - {N} → Rm, where N denotes the North Pole. Let Y be a vector field on the sphere Sm such that its restriction to Sm{N} equals (0-¹),X. What can you say about YN, the value of Y at the North Pole?See Answer
Q12:7.2 Vector Properties (#theoreticaltools) Determine whether the following statements are true or false. If true, provide a brief justification. If false, give a counterexample. (a) u v=vu for vectors u, in R³ (b) ||cu|cu|| for constant c in R and u in R³ = (c) u (vw) = uv-u w for vectors u,, w in R³ .See Answer
Q13:7.3 Heavy Metal(#differentiation) The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 3, 2) is 100°C. (a) Derive a function T(x, y, z) that gives the temperature in the ball at the point (x, y, z). (b) Find the rate of change of T at (1, 3, 2) in the direction toward the point (0,4, 2). (c) Show that at any point in the ball the direction of greatest increase in temper- ature is given by a vector that points toward the origin.See Answer
Q14:S.P. 2-I Find the value of Ads, where A = p²â+z² â¸, where S is the a cylinder of radius 2, centered along the z axis, and extending from z=0 to z=3. Also, what is the average value of A on this surface?See Answer
Q15:S.P. 2-H A vector field is given by: A = pcos² pâ, - pcosø sin pâ + zâ¸ . Find the flux A.ds, where S is the bounding surface of a cube over the range 0≤x≤2,0≤ y ≤2,0≤z≤2 SSee Answer
Q16:S.P. 2-F If A = cospâ, find the average value of A within a unit sphere centered at the origin.See Answer
Q17:Absolute Mad Lads - Raspux 00 PROBLEM SET 02: Vector Algeb x ←0 edfinity.com/assessments/6410be977b501400318446 edfinity ← PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center 13 10 Sensi 5 PROBLEM SET 02: Vector Algebra OPEN (b) 20-3D + 4R-6F R= Assuming the positive z-axis is horizontal and points to the right, find a vector R which solves the following equations (in terms of i, j). Use at least four decimal places when entering your answers. (a) 6Ď+4Ř= 5.F Ř= Submit answer Answers (in progress) de Answer 2 Cookies help us deliver our services. By using our services, you agree to our use of cookies. Score -/0.5 OK ㅁㅁㅁ I arn more Tumed in automatically when due ING 11:47 PM 9/2/2003See Answer
Q18:edfinity PH 221-2A. General Physics 1 (Fall 2023) Home ? Help Center M 10 Sonte mm/a 69°F Mostly cloudy PROBLEM SET 02: Vector Algebra OPEN 4. 5.0 53 A = 10.0 30 Search C-120 D-20.0 37 60 30 F-200 Cookies help us deliver our services. By using our services, you agree to our use of cookies. S Learn more Turned in automatically when due ENG 48 11:47 PM 1/2/2021 CSee Answer
Q19:edfinity ← Home ? Help Center 1 ¢ edfinity.com/assessments/6410be97765014003188446 PH 221-2A. General Physics 1 (Fall 2023) Sonte (0/41 PROBLEM SET 02: Vector Algebra OPEN 7. Practice similar Magnitude: Direction (north of east): components. (c) Reflect and convince yourself of how to use the method of components to solve this problem. (d) What are the magnitude and direction of the displacement needed to get the ball into the hole on the first putt? Submit answer ITEMS 4. m INFO A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.6 m exactly north. The second pur displaces the ball 2.2 m exactly southeast (i.e., 45 degrees south of east), and the third 0.8 m exactly southwest (i.e., 45 degrees south of west). What are the magnitude and direction of the displacement needed to get the ball into the hole on the first putt? (State direction as angle north of east). Suggested strategy: (a) Sketch the displacement vectors in such a way that you understand the big picture of what is happening. (b) Define a system of coordinates (i.e., the x and y axes) and redraw the displacement vectors so that it is easy to visualize their degrees Cookies help us deliver our services. By using our services, you agree to our use of cookies. OK Leam more *O! Turned in automatically when due ENG < Previous Next > 11:47 PM 9/2/2003See Answer
Q20:edfinity + PH 221-2A General Physics Home ? Help Center PROBLEM SET 02: Vector Algebra OPEN 6. (b) Displacement D=2-7j. Unit vector: Find the unit vector of direction (in terms of i, j) for the following vector quantities: (a) Force P-5+4j. Unit vector: I (c) Velocity=-41+7j. Unit vector: Submit answer Answers (in progress) Answer ITEMS 1 INFO D 0 Score Cookies help us deliver our services. By using our services, you agree to our use of cookies. -/0.17 Learn more ENG < Previous Next > 11:47 PM CSee Answer

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