(a) In cylindrical coordinates (2,6,2) the gradient of a scalar function (0, 0, 2) is given...
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Vector Fields A vector field has a more complicated derivative, because as you go from point to point in the field, you find that not only the magnitude of the vector can be changing, but also its direction Think of a vector field v(..); for instance, the flow velocity of a turbulent gas through some part of space. At each point, v has a certain magnitude and direction. Alternatively, we can split v up...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
PHYS 3043, Spring 19, HW#1 due Wed, Jan 23, by 3:00 pm 1) Show that sing + a) + sin侄-a)s cos(a) 2) (a) Given two vectors ธิ (2,2,1) and Ce(1,2,-6), what is xc? (b) Are B and C orthogonal to each other? How can you tell? 3) Given vectors A and E a) Define the dot product mathematically in two different ways. One way involving the components and the other the length/angles b)Define the vector cross product mathematically two different...