Page 74 - Engineering Mathematics Workbook_Final

Vector Calculus

(a) 16i − 9 j − 12k 137. The derivative of f(x, y) at point (1, 2) in
the direction of vector i + j is 2 2

−
(b) 16i − 9 j + 12k and in the direction of the vector 2 j is
-3. Then the derivative of f(x, y) in
(c) 16i − 9 j − 12k
direction i − − 2 j is
−
(d) 16i − 9 j + 12k
−
(a) 2 2 + 3 / 2 (b) 7 / 5
[GATE-2011 (PI)]
−
−
(c) 2 2 3 / 2 (d) 1/ 5
134. A particle, starting from origin at t = 0s,
is traveling along x-axis with velocity [GATE-95]

    138. The magnitude of the directional

V = cos   t m / s derivative of the function
 

2  2  f ( , x y = ) x + 2 3y in a direction
2
At t = 3s, the difference between the normal to the circle x + 2 y = 2 2 , at the
distance covered by the particle and the point (1, 1) is
magnitude of displacement from the
origin is _______ (a) 4 2 (b) 5 2

[GATE-2014]
(c) 7 2 (d) 9 2

[GATE-2000 (CE)]
135. A particle move along a curve whose
=
parametric equations are: x t + 3 2t , 139. The maximum value of the directional
derivative of the function
y = − 3e − 2t and z = 2 sin (5t), where x,  = 2x + 3y + 5z at a point
2
2
2
y and z show variations of the distance
covered by the particle (in cm) with time (1, 1, -1) is
t (in s). The magnitude of the
acceleration of the particle ( in cm s 2 ) (a) 10 (b) -4
/

at t = 0 is _________ (c) 152 (d) 152

[GATE-2014 (PI-SET 1)] [GATE-2002]
136. The smaller angle (in degrees) between 140. A scalar field is given by
+
the planes x + y z = 1 and f = x 2/3 + y 2/3 , where x and y are the
2x − + 2z = is _____
0
y
Cartesian coordinates. The derivate of ‘f’
[GATE-2017-EC SESSION-II] along the line y = x directed way from
the origin at the point (8, 8) is

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