Page 69 - Engineering Mathematics Workbook_Final

Vector Calculus

x + 2 y = 2 9 included in the first octant (c) (4/3  + + ) 2
) (a b c
5
0
between z = and z = where
(d) none
+
f = zi x j yzk .
−
96. Evaluate
(a) 40 (b) 60

(   x − yz ) i − 2x y j + 2k  n ds
2
3
(c) 80 (d) 100 S
where S denotes the surface of the
Volume Integral rectangular parallelepiped 0 x a  ,



0  y b, 0 z c is
93. Find     dV where  = xyz and
V 2
‘V’ is the volume of the region bounded (a) a bc (b) abc
by x = , y = , y = , z = x , z = . 3 3
0
2
0
6
4
3
ab c abc
(a) 162 (b) 172 (c) (d)
3 3
(c) 182 (d) 192

Stokes Theorem
Gauss – Divergence Theorem

−
97. Evaluate (e dx + x 2y dy dz ) where
94. Evaluate  f  n ds where S is the C
S ‘C’ is the curve x + 2 y = 2 4 and z = 2.
0
surface of tetrahedron bounded by x = ,
y = 0, z = and the place (a) 0 (b) 1
0
x + + = 1 and f = xyi z j + 2yzk (c) 2 (d) 3
+
2
z
y
3 1 98. Evaluate  f  dr where
(a) (b) C
8 8 f = (2x y i yz i yz j y zk− ) − 2 − 2 − 2 and

8 3 ‘C’ is the boundary of the upper half of
(c) (d) 2 2 2
2 5 surface of the sphere x + y + z = 1
above the xy-plane.
+
+
95. If f = ax i by j czk where a, b , c
(a) 0 (b) 1
are constants and ‘s’ is the surface of a
unit sphere then   f  n ds = (c) 2 (d) none
S
99. If  = 3x y y z then grade at (1, 2, 1− − )
−
3 2
2
(a) (4/3 ) (a b c + + )
is
(b) 0 a) 12i− − 9 j − 16k

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