Page 66 - Engineering Mathematics Workbook_Final

Vector Calculus

1 − (b) 2i + 4 j + k
(a) (b) 0
6
  1  

1 (c)     (2i + 4 j − ) k
(c) (d) 6  21 
6
(d) none
[IISC 2006]
73. If the temperature at any point in space
3 is given by T = xy + +
R
70. Let : f R → be defined yz zx , then the
( , , y z =
2
4
2
f x ) x + 2xy + 5y − z − 1. directional derivative of T in the
direction of the vector 3i − 4k at
The unit vector u which gives the
maximum value for the directional (1, 1, 1) is
derivative D f at the point (1, 0, 1) is
u 2 1
_______ (a) − (b)
5 5
(a) u = (1, 0, 0)
5 5
(b) u = (0, 0, 1) (c) (d) −
2 2
− 1
)
(c) u = (1,0,1 In what direction from (3, 1, −
2 74. ) 2 ,
the directional derivative of
1 2 2 4
x
(d) u = (1,1, 2− ) [IISC 2006]  ( , , y z =
) x y z is maximum?
6
(a) (
71. Find the gradient of the function 96 i + 3j − 3k )
 = x − 2xy + z at the point
2
2
96 i −
(2, 1,1− ) . (b) ( 3j + 3k )

96 i −
(a) 6i − 4 j + 2k (b) 4i − 6 j + 2k (c) ( 3j − 3k )

(c) 6i + 4 j − 2k (d) 6i − 4 j − 2k (d) (
48 i − 3 j + 3k )
72. A unit normal to the surface z = 2xy at

the point (2, 1, 4) is Divergence

75. The divergence of
+
x zi − 2 2y z j xy k at the point
2
3
2

(1,1, 1− ) is
−
(a) 2i + 4 j k

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