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Engineering Mathematics
Vector Calculus Basic
Quiz 1
Solution
Q.1.
Del operator is also known as _________
a) Divergence operator
b) Gradient operator
c) Curl operator
d) Laplacian operator
Q.2.
The gradient of a scalar field V is a vector that represents both magnitude and the direction of the maximum space rate of increase of V.
a) True
b) False
Q.3.
The gradient is taken on a _________
a) tensor
b) vector
c) scalar
d) anything
Q.4.
Find the gradient of a function V if V= xyz.
a) yz ax + xz ay + xy az
b) yz ax + xy ay + xz az
c) yx ax + yz ay + zx az
d) xyz ax + xy ay + yz az
Q.5.
Find the gradient of V = x2 sin(y)cos(z).
a) 2x siny cos z ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
b) 2x siny cos z ax + x2 cos(y)cos(z) ay + x2 sin(y)sin(z) az
c) 2x sinz cos y ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
d) x siny cos z ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
Q.6.
Find the gradient of the function W if W = ρzcos(ϕ) if W is in cylindrical coordinates.
a) zcos(ϕ)aρ – z sin(ϕ) aΦ + ρcos(ϕ) az
b) zcos(ϕ)aρ – sin(ϕ) aΦ + cos(ϕ) az
c) zcos(ϕ)aρ + z sin(ϕ) aΦ + ρcos(ϕ) az
d) zcos(ϕ)aρ + z sin(ϕ) aΦ + cos(ϕ) az
Q.7.
If W = xy + yz + z, find directional derivative of W at (1,-2,in the direction towards the point (3,6,9).
a) -0.6
b) -0.7
c) -0.8
d) -0.9
Q.8.
Electric field E can be written as _________
a) -Gradient of V
b) -Laplacian of V
c) Gradient of V
d) Laplacian of V
Q.9.
Let F = (xyax + yx2 ay, F is a not a conservative vector.
a) True
b) False
Q.10.
State whether the given equation is a conservative vector.
a) True
b) False
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