‎BIA004 (2016)‏ لم

‎planes and the planex +y+z= 1
PART C
(Each question carries 5 Marks)

‎Answer any THREE questions

‎19 Find div F and curl F of F(x, y,z) = x*yi + 2y3zj + 3zk
20 Show that एर (कष) = 1 (7 + 1272 wherer = || + yj + 2/८ |
21 Find the work done by the force field

‎F(x,y,z) = (x? +xy) i+ (y—x*y)j ‏ہہ‎ a particle that moves
along the curve (~: = ‏برع‎ = : ,1 > > 3

‎22 Evaluate | ¢. दौ where F(x, 9) ‏برع‎ { - x j along the triangle joining
the vertices (0.0), (1.0). and (0.1).

‎23 Determine whether F(x, 9) = 4y { + 4x/ is a conservative vector held, ||

‎so, find the potential function and the potential energy.
Answer any THREE questions

‎24 Using വട theorem evaluate ழ்‌. (€+ + 12) dx + (€” + ८) dy)

‎where C is the boundary of the region between y = x? andy = 2x.
८२

‎= 5 वि 8 a + 5 ۹ 1
25 Evaluate the 511118८6 integral | f° “dS over the surface

‎y
‎orepresented by the vector valued function
r(u,v) = 2cosvitujt2sinvk,lsus3, 00௩

‎26 Using Divergence Theorem evaluate Sf, Fin 09 where F(x, y,2) =
(> - ‏بو) + زوج‎ (മമ. is the surface of the cylindrical
solid bounded by ‏قير‎ +y*=a?,z=0,z2=1.

‎27 Determine whether the vector field F (x,y,z) = 40-൮൧
40൮ ಬಲಿ —z)k is free of sources and sinks. 1 it is not.
locate them,

‎28 Using Stokes theorem evaluate J 1. dr where
F(x, ೫,೩) = x°i + ಓ೧ 1 t+ 2×۷
(` is the rectangle: 0 > x > 1,0 < + = 3 in the plane = y

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