Page 70 - Engineering Mathematics Workbook_Final

Vector Calculus

b) 12i − 9 j − 16k of 2i − j − 2k is

c) 12i + 9 j + 16k 37 14
(a) (b)
−
d) 12i + 9 j + 16k 3 3
100. The unit normal vector to the surface (c) 28 (d) 2

 : x − y + x zat (1,1, 2 is 3
)
3
3
2
−
107. The directional derivative of
i − − 3 j k i − 3 j + k
+
(a) (b)  ( ,x y = ) x )
11 11 x + y 2 at the point (0,2 along a
2
−
i + 3 j + k i + 3 j k 0
(c) (d) line making angle 30 . With the positive
11 11
direction of x axis is
101. The greatest value of directional derivative
3 3
)
of xy + yz at (2, 1,1 is (a) 8 (b) 4
2
3
−
(a) 19 (b) 2 19 3 1
(c) (d) 8
(c) 11 (d) 2 11 2
2 2
 1  108. The directional derivative of x + y at
3
3
102. The value of  2       = _____ where r is the
 r 
8,8
( ) along the line y = directed away
x
position vector of any point.
from the origin is ____
(a) 0 (b) 1
3 3
(c) 2 (d)3 (a) (b)
2 2
103. If F = ( x + 3y ) i + ( y + 2z ) j + ( x + pz ) k is
2 2
solenoidal vector then the value of P =____ (c) (d)
3 3
(a) 0 (b) 1
109. Let ( , x y = − 3 − 3
f
) kxy x y xy where K is real
(c) 2 (d) -2
n
104. If F = r r is solvenoidal then n = ______ constant. If the directional derivative of f at
(a) -1 (b) -2 point (1,2) in the direction of a unit vector
(c) -3 (d) -4 1 1 15
− i − j is then the value of K is

105. If F = r and .F = 0then n = ___ 2 2 2
n
____
(a) -1 (b) -2
(a) 2 (b) 4
(c) -3 (d) -4
(c) 1 (d) -2
106. The directional derivative of surface

2
 : x yz + 2 4xz at (1, 2, 1− − )in the direction

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