
i) Consider the following position vector: r = x + y + z2. Convert this position...
Consider the given vector field. F(x, y, z) = (9 / sqrt(x2 + y2 + z2)) (x i + y j + z k) Find the curl of the vector field. Then find Divergence
Consider the vector field F (x, y, z) = <y?, z2, x?>. Compute the curl (F). Use Stokes' Theorem to evaluate S. F. dr where C is the triangle (0,0,0), (1,0,0), and (0, 1, 1) oriented counter-clockwise when viewed from above.
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of a new coordinate system, x= x(u, v, w), y=y(u, v, w), z=z(u, v, w). Let r(s) = x(s) i+y(s) + z(s) k be the position vector defining some continuous path as a function of the arc length. Similarly for the other partial derivatives in v and w. For spherical coordinates the following must also be true for any points, x = Rsin o cose,...
Write a MATLAB code that can convert a vector in any coordinate system to the other two coordinate systems. The code must ask the use to select in which coordinate system is the entered data. Write a MATLAB code that can convert a vector in any coordinate system (Cartesian, cylindrical or spherical) to the other two coordinate systems. The code must ask the use to select in which coordinate system is the entered data.
515P) Calculate (r is the usual position vector): 7:7, 7(r-), r •7(r) integrate this over a spherical volume radius b centered at origin: convert this to surface and volume integral.
Notation and convention: r x +y The distance from the origin to the point r [x,y,z] + ê: The unit vector along the direction of r-[x, y,z] (a.e,6)-i.j.):m :The orthonormal bases of a Cartesian coordinate system. for dummy indices Einstein convention: Omitting the summation notation (repeated indices). Examples:ab,-a b, ab a b Notice: No dummy index is allowed to be repeated more than twice. You should change the "names" of the dummy indices before taking the product of two summations...
The position vector of a point which moves in the x-y plane is given by: r = (- 0.2 t4 + 1.8 t3 + 1.1 t2) i + (- 0.4 t4 - 1.2 t) j where r is in meters and t is in seconds. Determine the angle between the velocity v and the acceleration a when t = 1.7 sec.
Practice: 1. A vector defined at (4,0,0) is expressed in Cartesian coordinate system as (2,3,0), convert it into cylindrical and spherical representations; 2. If the same vector is moved to (4,0,1), what are its cylindrical and spherical representations?
A position vector r has the following x and y components: r_x = 12.2 m r_y= 7.5 m. What is the direction of this vector? Give your answer as an angle measured counterclockwise from the +x direction. What is the magnitude of this vector? If you doubled both the x and y components of this vector, how would the answers to parts (a) and (b) change? The direction would remain the same, but the magnitude would increase by a factor...
Given that z1 = 6−3 i and z2 = 3−11 i, find the following in the form x + y i _ Z1 = _ Z1 Z2 = Z1/Z2=