22. Q. Find the directional derivative of
φ = 4 e2x−y+z
at the point (1,1,-1) in the direction towards
the point (-3,5,6)
23. Q. The vector that is normal to the surface 2xz2 –
3xy – 4x = 7 at the point (1, -1, 2) is
A. 2i – 3j + 8k
B. 2i + 3j + 4k
C. 7i – 3j + 8k
D. 7i – 5j + 8k
24. Q. Find the values of a, b and c such that the
directional derivative of
at (1,2,-1) has the maximum magnitude 64 in
the direction parallel to z-axis
2 2 3
axy byz cz x
25.
26. Q. Find the constants a and b such that the surface
will be orthogonal to the surface
at the point (1,-1,2)
2
ax byz (a 2)x
2 3
4x y z 4
27.
28. Q. Find the directional derivative of
𝛗 = 𝐱𝐲𝟐
+ 𝐲𝐳𝟑
at the point (2,-1,1) in the direction of
normal to the surface
at the point (-1,2,1)
2
e
x.log z y
29.
30. Q. For a position vector r = xi+ yj+ zk the norm of
the vector can be defined r = x2 + y2 + z2.
Given a function ϕ = 𝓁n r , its gradient ∇ϕ is ___.
A. r
B.
r
|r|
C.
r
r⋅r
D. 𝑟
𝑟
3
31. Q. The value of the directional derivative
of the function ϕ(x, y, z) = xy2 + yz2 + zx2
at the point (2, -1, 1) in the direction of
the vector P = i + 2j + 2k is
A. 1
B. 0.95
C. 0.93
D. 0.9
32. Q. Directional derivative of ϕ = 2xy-y2 at
the point (1, 3, 2) becomes maximum
in the direction of __________
36. Q. Find the directional derivative of
in the direction of
𝟏
𝒓
𝒓
37. Q. The magnitude of the directional derivative
of the function f(x, y) = + 3y2 in a
direction normal to the circle x2 + y2 = 2, at
the point (1, 1) is
A. 4 2 B. 5 2
C. 7 2 D. 9 2
𝑥2
38.
39. Q. The directional derivative of f =
y
x2+y2 at
P(0, 1) along the line which makes an angle
30° with positive x-axis is
A. –1/2
B. 1/2
C. 1/3
D. None
40.
41. Q. If r = xi+ yj+ zk and r = r then
∇
1
r
=
A.
−r
r3
B.
r
r3
C.
−r
r
D. −r
r2
