vector calculus questions and answers pdf

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Calculate the integral of f(x, y, z) = 5x^2 + 5y^2 + z^2 over the curve c(t) = (cos t, sin t, t) for 0 less than or equal to t less than or equal to pi. C: x-axis from x=0 to x=3, Evaluate integral_C (2 x - y) dx + (x + 4 y) dy. VECTOR AND METRIC PROPERTIES of Rn 171 22.1. Evaluate the line integral \int_C {2ydx + 4xdy} where C is the straight-line path from (3, 1) to (5, 4). Evaluate the line integral \int_C y^3dx-x^3dy, where C is the circle x^2 + y^2=4. a. Evaluate the line integral, where C is the given curve. Evaluate I = \int_{C} (\sin x + 3y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. Use Green's Theorem to compute the integral \int_C (x^2y + x) dy + y^2xdx where C is the semi-circle x^2 + y^2 = 209 and y \geq 0. There is no answer key for vector calculus previous year question paper can u old post, Answer for vector calculus previous year question paper. Compute the following: A. div F = \boxed{\space}\\ B. curl F = \boxed{\space} i + \boxed{\space} j + \boxed{\space}k \\ C. div curl F = \boxed{\space}. Find the line integral along the path C shown in the figure below. All rights reserved. Consider the given vector field. © copyright 2003-2020 Study.com. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. A third vector, vector C, lies in the xy-plane. As a partial check, |v(1)| = \sqrt{30}, Evaluate the line integral c F d r , where C is given by the vector function r ( t ) F ( x , y , z ) = x i + y j + x y k , r t ) = cos t i + sin t j + t k , 0 t. Evaluate the line integral, where C is the given curve. Let F(x, y, z) = (x2 + y2)i + 2xyj + xyzk, (a) Find curl F. (b) Find div F. Let C be the curve represented by r(t) = ti + t^2 j, for t between 0 and 1. u = cos (pi / 3) i + sin (pi / 3) j, v = cos (3pi / 4) i + sin (3pi / 4) j. Compute the divergence of the vector field 33 sin (21 x^{13} + z^{13}) i + 21 y^9 j - 21 y e^{13 x z} k. (Use symbolic notation and fractions where needed. Previous Year Questions PDF … div F = _____. False. A motorboat is set to head northeast from the mainland to a near island, lying approximately 15 km away. Suppose a = 4i - 3j, b = \left \langle -2, 1 \right \rangle,\ and\ c = \left \langle 1, -2 \right \rangle Write vector a in trigonometric form. Evaluate the line integral integral_C F . Candidates can download Vector Calculus Study Materials along with Previous Year Questions PDF from below mentioned links. Use Green's Theorem to compute the integral \int_C (x^2y+x)dy +y^2xdx where C is the semi-circle x^2+y^2 = 209 and y \geq 0. Evaluate the line integral \int_C3xy^4 ds, where C is the right half of the circle x^2 + y^2 = 9. Compute the line integral: int C (x2 + y2 + z2) ds where C is the curve r(t) = (sin t, cos t, t), 0 leq t leq 3pi/4. For a normal distribution with mean of 2500 and standard deviation of 500, what percentage is less than 2500? Let F = (3yz)i + (8xz)j + (8xy)k. Compute the divergence, the curl, and divergence curl. 1 C. 1/3 D. -1/3 E. None of the above. Evaluate the line integral C F d r where C is given by the vector function r ( t ) . Apply Green's Theorem to evaluate the integral. Write v in terms of i and j . F(x, y, z) = xye^zi + yze^xk, Find (a) the curl and (b) the divergence of the vector field. Let \vec{F}(x, y, z) = xyz i -x^2y k. Find the curl and the divergence of \vec F. Find the integral of F = 3xyi + x^2j around the rectangle as shown on the figure, counterclockwise. Let F = (14xyz + 7 sin x, 7x^2z, 7x^2y). integral_C x y dx + (x - y) dy, C consists of line segments from (0, 0) to (3, 0) and from (3, 0) to (4, 2). Evaluate the line integral, where C is the given curve. Evaluate the integral of F along the following path. Thus!v 0 = 1 p 2 b 1 p 2 … C: x-axis from x = 0 to x = 9. Previous Year Questions PDF Download Let u = 6\hat i \times 7\hat j \text{ and } v = \hat j \times \hat k. Compute u \times v \text{ and } v \times u. What is the overall magnitude of the force you're applying? Calculate integral_C xy + 2 ds, where C is the line segment from (1, 1) to (2, -1). Evaluate the line integral, where C is the given curve. Evaluate int_C xydx + (x^2 + y^2)dy where C is the square with vertices (0,0), (0,1), (1,0), and (1,1) oriented counterclockwise. If it is conservative, find a function f such that F = bigtriangledown f. F(x, y, z) = 10xy i + (5x2 + 4yz) j+ 2y2 k, Evaluate the line integral, where C is the given curve. \int_C xyz^2 ds, C is the line segment from (-2, 3, 0) to (0, 4, 1). Represent the plane curve \dfrac{x^2}{16} -\dfrac{y^2}{4} = 1 by a vector-valued function. If it is conservative, find a function f such that F = f . Evaluate the line integral \int_C {{\bf{F}} \cdot d{\bf{r}}}. ), Find two unit vectors orthogonal to both \left \langle6, 2,1\right \rangle and \left \langle-1, 1, 0\right \rangle. MATH 20550: Calculus III Practice Exam 1 Multiple Choice Problems 1. Find a function f so that F = ∇f, and f(0, 0, 0) = 0. Evaluate \int_C \dfrac{1}{1 + x} ds, where C is the arc of the curve y = {2/3}x^{3/2} from the point P(0, 0) to the the point Q(3, 2\sqrt{3}). Exams Daily – India's no 1 Education Portal, RRB Railway NTPC  Aptitude NUMBER SYSTEM Quiz, National Insignia Quiz – Check Questions & Answers, Railway Group D Level 1 General Science Quiz, TN Police Constable Free Test Available | Check TNUSRB PC Model…, TNUSRB Police Constable Previous Question Paper, WB JELET Previous Year Question Paper (OUT), Ratio and Proportion Aptitude Tricks PDF – For Competitive Exam, Quadratic Equation Questions & Answers PDF Download, Static GK topics for Competitive Exams – Check Static GK Competitive…, Problem Solving Reasoning Questions and Answers PDF, APPSC Departmental Test Answer Key 2020 – Check May Session Solution…, WBHRB Tutor Interview Call Letter 2020 (OUT) – Download Schedule Here…, CSIR CSIO Recruitment 2020 Released – Apply for Project Assistant, Project…, TNPSC Group 2 Counselling Memo 2020 Link Out – CCSE Phase…, DSSSB Drawing Teacher Result 2020 Released – Download Merit List @…. \int_{c}ydx + xdy = \boxed{\space}. d\vec{r} for \vec{F} = - 4y\vec{i} - x\vec{j} - 4z\vec{k}. Calculate Integral_{C} xy dx + (x+y) dy, where C is the path from (-1,1) to (2,4) along y=x^2. Evaluate int (x+y) ds over C, a line segment from (0,2,0) to (2,0,0). Calculate the line integral where f(x, y) = x + yz is a scalar function, and C is the line segment from (0, 1, 0) to (1, 0, 1). Find the curl and the divergence of the vector field. F(x, y, z) = \frac{1}{\sqrt{x^2 + y^2 + z^2}}(xi + yj + zk), Find (a) the curl and (b) the divergence of the vector field. Find curl F. Use Green's Theorem to evaluate \int_C F. dr. (Check the orientation of the curve before applying the theorem.) where F(x,y,z) = - 2\sin x{\bf{i}} - 3\cos y{\bf{j}} - xz{\bf{k}} and C is given by the vector function r(t) = {t^3}{\bf{i}} - {t^2}{\... You're pushing a shopping cart with a 20 N force downwards and a 50 N force forwards.

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