Page 67 - Engineering Mathematics Workbook_Final

Vector Calculus

2
(a) 8 − (b) 3 (a)  (b) 

2
(c) 3 (d) 2 (c) 2 (d) 2
76. The value of p for which the vector field Vector Identities
V = (2x + y i + 2z ) j + (x + pz )k
) (3x −
j
y
is solenodial 80. If F = (x + + ) 1 i + − (x + ) y k
then  (
(a) 0 (b) 2  F ) =

(c) 2− (d) 1 (a) zero (b) F

(c) 2 (d) None

Curl
+
+
=
81. If r xi y j zk and r = r then
77. If the velocity vector in a two- grad (1/ r) is
dimensional flow fluid is given by
V = 2xy i + (2y − x 2 ) j then the curl (a) r (b) r
2
r 2 r 3
V will be
r r
(c) − (d) −
(a) 2y j (b) 6yk r 2 r 3

−
(c) zero (d) 4xk If r xi y j zk= + + and r =
82. r then
78. The value of a, b, c for which  r 

V = (x + + ) (bx + 3y − ) z j div   r 3    =
y az i +
)
+
+
+ (3x cy z k is an irrotational.  
(a) 0 (b) 1
(a) a = 1, b = 3, c = 1
−
(c) 1 (d) 2
3
(b) a = 1, b = 1, c =
+
=
+
83. If r xi y j zk and r = r then
(c) a = 3, b = 1, c = − 1
( )
n
curl r r =
(d) None
79. A rigid body is rotating with constant (a) 0 (b) 1−
angular velocity  about a fixed axis. If
V is the velocity of a point of the body (c) r (d) r
then curl V is equal to

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