Page 55 - Engineering Mathematics Workbook_Final

Vector Calculus
r r
)
$
$
$
2
2
z
1. Let r = ( x i + y j + zk and r = r . If x + y − = 0 and the plane
1 x z + 3 = at the point (1, 1, 2) passes
f r = g , r  0,
( ) ln r and ( ) r =
r through
satisfy 2 f  + h ( ) r  = , then h(r) is (a) (-1, -2, 4) (b) (-1, 4, 4)
0
g
(c) (3, 4, 4) (d) (-1, 4, 0)
1
(a) r (b)
r [JAM MA 2019]
(c) 2r (d) 3
R
5. Let : f R → be defined by
[JAM MA 2016] y
( , , y z =
2
f x ) sin x + 2e + z
2
2. The tangent plane to the surface
z = x + 2 3y at (1, 1, 2) is given by The maximum of change of f at
2
  

+
(a) x − 3y z = 0   4 ,0,1 , correct upto three decimal

 


(b) x + 3y − 2z = 0 places, is _______
0
(c) 2x + 4y − 3z = [JAM MA 2015]
0
(d) 3x − 7y + 2z = 6. Let
[JAM MA 2018]  x + y 3 , x − 2 y  2 0
3

 
)
2
3
3. In R , the cosine of the acute angle f ( , x y =  x − y 2

between the surfaces  0, x − 2 y = 2 0


x + y + z − =
2
2
2
9 0 and
−
z x − y + = Then the directional derivative of f at
2
2
3 0 at the point
4 $ 3 $
(0, 0) in the direction of i + j is
(2, 1, 2) is 5 5
8 10 ________.
(a) (b)
5 21 5 21 [JAM MA 2019]
8 10 r r
(c) (d) 7. For a constant vector a and r
3 21 3 21 r $ $ $
r = x i + y j + zk , consider the
[JAM MA 2018] following statements:
r r r r
(

curl a r =
4. The tangent line to the curve of (I) (  ) 2grad a r )
intersection of the surface

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