Suppose F(x, y) = -yi + xj and C is the line segment from point P = (5,0) to Q = (0, 3).(a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond to t = 0 and t = 1, respectively.r(t) = <5-5t, 3t>(b) Using the parametrization in part (a), the line integral of F along C isF. dr =| FG() · F'(1) dt =dtwith limits of integration a =and b =1(c) Evaluate the line integral in part (b).15(d) What is the line integral of F around the clockwise-oriented triangle with corners at the origin, P, and Q? Hint: Sketch the vectorfield and the triangle.15/2

Given that F→=-yi→+xj→ is the line segment from P=(5,0) to Q=(0,3). (a) A vector parametric equation…

Suppose F(x, y) = -yi + xj and C is the line segment from point P = (5,0) to Q = (0, 3). (a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond to t = 0 andt = 1, respectively. F(1) = <5-5t, 3t> (b) Using the parametrization in part (a), the line integral of F along C is b · dr = / " FG4) · F'() dt =/ dt C with limits of integration a = and b = 1 (c) Evaluate the line integral in part (b). 15 (d) What is the line integral of F around the clockwise-oriented triangle with corners at the origin, P, and Q? Hint: Sketch the vector field and the triangle.

Suppose F(x, y) = -yi + xj and C is the line segment from point P = (5,0) to Q = (0, 3). (a) Find a vector parametric equation r(t) for the line segment C so that points P and Q correspond to t = 0 andt = 1, respectively. F(1) = <5-5t, 3t> (b) Using the parametrization in part (a), the line integral of F along C is b · dr = / " FG4) · F'() dt =/ dt C with limits of integration a = and b = 1 (c) Evaluate the line integral in part (b). 15 (d) What is the line integral of F around the clockwise-oriented triangle with corners at the origin, P, and Q? Hint: Sketch the vector field and the triangle.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

See similar textbooks

Similar questions

What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?
Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.
Give a scalar equation for a plane at distance 9 from the plane P with equation 2x−2y−z = 4. 0
Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?
Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.
Find the scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to the line of intersection of planes x + y − z − 2 = 0 and 2x − y + 3z − 1 = 0.
Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)
Find a parametrization for the line segment beginning at P1 and ending at P2. P 1(-4, 0, 3) and P 2(0, 5, 0) a)x = -4t, y = -5t + 5, z = 3t, 0 ≤ t ≤ 1 b) x = 5t, y = -4t + 5, z = -2t, 0 ≤ t ≤ 1 c) x = 5t - 4, y = -4t, z = -2t + 3, 0 ≤ t ≤ 1 d) x = 4t - 4, y = 5t, z = -3t + 3, 0 ≤ t ≤ 1
give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 1
Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1) that is parallel to the plane 3x−2y −z −4 = 0 and perpendicular to the line 2x = −y/2 = −3z.
generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then generate another parametrization of the line using the point P2(-2, -2, 1) and the vector v2 =-i + (1/2)j - (3/2)k.
Find a vector function that represents the curve of the intersection of the two surfaces. The paraboloid z=4x2+y2 and the parabolic cylinder y=x2