Free Printable Vector Analysis

1.

Choose all the correct answers:

A vector A is a quantity which

a)

Has magnitude

b)

Has direction

c)

Adds according to the parallelogram law

d)

Is independent of the coordinate system

2.

The dot product $\left(1,\ -2,\ 2\right)\cdot\left(-1,\ 1,\ 3\right)$ is equal to

a)

0

b)

3

c)

9

d)

None of the above

3.

A $\cdot$ B = 0 means that

a)

A and B are colinear

b)

A and B are parallel

c)

A and B are perpendicular

d)

None of the above

4.

A quantity that has both magnitude and direction is called a scalar quantity.

a)

True

b)

False

5.

The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.

a)

True

b)

False

6.

A vector is said to be solenoidal when its

a)

a) Divergence is zero

b)

b) Divergence is unity

c)

c) Curl is zero

d)

d) Curl is unity

7.

A field has zero divergence and it has curls. The field is said to be

a)

a) Divergent, rotational

b)

b) Solenoidal, rotational

c)

c) Solenoidal, irrotational

d)

d) Divergent, irrotational

8.

The volume integral is three dimensional. State True/False

a)

True

b)

False

9.

$\nabla.\overrightarrow{\ r\ \ }\ =x\ \overline{i}\ +y\ \overline{i}\ +z\ \overline{k}$ , or div $\overrightarrow{\ r\ }$ =

a)

3

b)

1

c)

2

d)

$\overrightarrow{\ r\ }$

10.

$\int_A^B\overrightarrow{f\ }.d\ \overrightarrow{r\ }$ is,

a)

Volume integral

b)

Surface integral

c)

Line integral

d)

None of the above

11.

$\overrightarrow{\ f\ }$ is irrotational if following hold

a)

$\nabla\times\overrightarrow{\ f\ }=1$

b)

$\nabla.\overrightarrow{\ f\ }=0$

c)

$\nabla\times\overrightarrow{\ f\ }=0$

d)

$\nabla\cdot\overrightarrow{\ f\ }=1$

12.

$\overrightarrow{\ f\ }$ is solenoidal if following hold

a)

$\nabla\times\overrightarrow{\ f\ }=1$

b)

$\nabla.\overrightarrow{\ f\ }=0$

c)

$\nabla\times\overrightarrow{\ f\ }=0$

d)

$\nabla\cdot\overrightarrow{\ f\ }=1$

13.

Physical meaning of gradient is

a)

change in a definite direction

b)

change in any direction

c)

radical change in any direction

d)

radical change in a definite direction

14.

divergence of a vector means

a)

flow of a vector

b)

net flow of a vector over a surface

c)

net flow of a vector from a volume element

d)

outward flow of a vector

15.

curl of a vector means

a)

vorticity or rotation of a scalar

b)

vorticity or rotation of a vector

c)

rotation of a scalar or vector

d)

rotation of any object

16.

Guss's theorem of vector calculus connects

a)

volume integral with surface integral

b)

surface integral of divergence of a vector with volm integral of a scalar

c)

surface integral of divergence of a vector with volm integral of the same vector

d)

surface integral of divergence of a vector with volm integral of a different vector

17.

Surface integral of curl of a vector is connected with its line integral through

a)

Green's theorem

b)

Stoke's theorem

c)

Guass's theorem

d)

Laplace's theorem

18.

When two vectors are perpendicular, their

a)

a) Dot product is zero

b)

b) Cross product is zero

c)

c) Both are zero

d)

d) Both are not necessarily zero

19.

The Stoke’s theorem uses which of the following operation?

a)

a) Divergence

b)

b) Gradient

c)

c) Curl

d)

d) Laplacian

20.

Surface integral is used to compute

a)

a) Surface

b)

b) Area

c)

c) Volume

d)

d) density

21.

The triple integral is used to compute volume.

a)

True

b)

False

22.

The gradient of xi + yj + zk is

a)

0

b)

1

c)

2

d)

3

23.

Curl of gradient of a vector is

a)

Unity

b)

Non Zero

c)

Null Vector

d)

None of the above

24.

The maximum rate of change of a scalar field F in space is given by

a)

The magnitude of the gradient of the field F

b)

The magnitude of the divergence of the field F

c)

The magnitude of the curl of the field F

d)

none

25.

Del operator is also known as ---------------

a)

Divergence operator

b)

Gradient operator

c)

Curl operator

d)

Laplacian operator

Vector Analysis

Total questions: 25

Worksheet time: 53mins

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