WorksheetsVector Calculus Multiple Choice Questions
Total questions: 10
Worksheet time: 5mins
Name
Class
Date
1.
If f = 3x + x^2y + yz, then the grad f at the point (1,0,2) is
a)
5i + 2j + k
b)
5i - 2j - k
c)
3i + 3j
d)
6
2.
If r = xi+yj+zk and r = |r|, then ∇rn is
a)
5i + 2j + k
b)
rn−2r
c)
2i + 2j + 2k
d)
nrn−2r
3.
If φ = xyz, then the grad φ at the point (1,1,1) is
a)
i + j + k
b)
3i + 3j + 3k
c)
i - 3j
d)
i - j - k
4.
The divergence of a vector is a
a)
Scalar Quantity
b)
Vector Quantity
c)
Constant
d)
zero
5.
The curl of a vector is a
a)
Scalar Quantity
b)
Vector Quantity
c)
Constant
d)
zero
6.
If a vector F is solenoidal then
a)
∇·F = 0
b)
∇×F = 0
c)
∇F = 0
d)
None of the above
7.
If F = x2i+y2j+z2k , then F at (1,1,2) is
a)
Solenoidal
b)
5i - 2j - k
c)
Not Solenoidal
d)
None of the above
8.
If F is conservative, then
a)
∇·F = 0
b)
∇×F = 0
c)
∇F = 0
d)
None of the above
9.
∇×r is
a)
r
b)
2r
c)
0
d)
i + j + k
10.
Find a unit vector normal to the surface x2+y2−z=10 at (1,1,1).
a)
1
b)
2
c)
0
d)
None of the above
100 %
