Page 75 - Engineering Mathematics Workbook_Final

Vector Calculus

2 3 (c) -3 (d) 3
(a) (b)
3 2 [GATE-99]

2 3 If F = n
(c) (d) 144. r r is solenoidal then n =
3 2 ______

[GATE-2005 (IN)] (a) -1 (b) -2

141. A sphere of unit radius is centred at the (c) -3 (d) -4
origin. The unit normal at a point (x, y, [GATE]
z) on the surface of the sphere is the
vector.  1 
145. The value of  2       = ______ where
(a) (x, y, z)  r 

 1 1 1  r is the position vector of any point. If
(b)   , ,     F = r and  F = 0 then n =
n
 3 3 3 
_________ [GATE]
 x y z 
(c)   , ,     If r = xa x + ya y + za r
$
$
$
 3 3 3  146. z and r = ,
 x y z  then div r  2 (ln r = ) _____
(d)   , ,    
 2 2 2  [GATE-2014 (EC-SET 2)]

[GATE-2009 (IN)]

$
$
$
142. The directional derivative of 147. For a position vector r = x i + y j + zk
f ( , x y = ) xy (x + ) y at (1, 1) in the the norm of the vector can be defined as
2 r − x + y + 2
2
2
direction of the unit vector at an angle of z . Given a function
  = 
with y-axis, is given by ….. ln r , its gradient  is
4

[2014-EC-SEC 4] (a) r (b) r
r
3
143. For the function  = ax y − 2 y to
represent the velocity potential of an r r
ideal fluid,  2 should be equal to zero. (c) r r (d) r 3

In that case, the value of ‘a’ has to be

(a) -1 (b) 1 [GATE-2018 (ME-AFTERNOON
SESSION)]

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