For the following problem, show your work clearly and completely (in detail). Pa

Question

For the following problem, show your work clearly and completely (in detail). Partial credit will be awarded for correct and applicable work. If A = 2yzi - x^2yj + xz^2k, B = x^2i + yzj - xyk and phi = 2x^2yz^3, find (a) (B middot nambla) A, and (b) A times nambla phi. Find the work done in moving a particle once around a circle C in the xy plane, if the circle has centre at the origin and radius 3, and if the force field is given by F = (2x - y + z)i + (i + y - z^2)j + (3x - 2y + 4z)k. Evaluate integral integral_S F middot n ds, where F = xyi + 2yzj + 3zxk and S is the surface of the cube bounded by x = 0, x = 2, y = 0, y = 2, z = 0, z = 2. By multiplying both sides of the equations by a differentiable functions f(x) and then integrating over x, prove that partial integral(-x) = partial integral(x).

Explanation / Answer

1)   a) 2xy i - xz j - yz k

      b)   2x2 i - xy j - xz k

2)    Work done   = sqrt( 42 + 82 + 52)

                          = 10.247 J

3)    F.n ds    =   (22 * 1) + (2 * 1 * 1) + (3 * 2 * 1)

                     = 12

4)   delta(x)   =   x2 + 2x4 - 4x6

=>   delta(-x) = delta(x)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.