Free Printable Vector Differentiation

1.

$i\times\left(\overrightarrow{\ a\ }\times i\right)+j\times\left(\overrightarrow{\ a\ }\times j\right)+k\times\left(\overrightarrow{\ a\ }\times k\right)=$

a)

0

b)

$\overrightarrow{\ a\ }$

c)

$2\overrightarrow{\ a\ }$

d)

3

2.

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

a)

3

b)

1

c)

2

d)

$\overrightarrow{\ r\ }$

3.

$\nabla^2\psi\left(x,y,z\right)=0,\$ the function $\psi$ is

a)

Solenoidal

b)

Irrotational

c)

Harmonic

d)

None of the above

4.

$r=\left|\overrightarrow{\ r\ }\right|,\overrightarrow{\ r\ }=xi+yj+zk,\ then\ \nabla r$

a)

$r^2$

b)

$\overrightarrow{\ r\ }$

c)

$r^3$

d)

$\frac{\overrightarrow{\ r\ }}{r}$

5.

$\nabla\cdot\left(\nabla\times\overrightarrow{F}\right)$
What will this operation result in?

a)

Scalar function

b)

Vector function

c)

Undefined

d)

$\overrightarrow{\ F\ }$

6.

$\nabla\times\left(\nabla\cdot\overrightarrow{F}\right)$
What will this operation result in?

a)

Scalar function

b)

Vector function

c)

Undefined

7.

$\nabla\times\left(\nabla\times\overrightarrow{F}\right)=$
What will this operation result in?

a)

Scalar function

b)

Vector function

c)

Undefined

d)

Stoke's Theorem

8.

Find div $\overrightarrow{F}$ : $\overrightarrow{F}\left(x,y,z\right)=<x^2,\ y-z,\ xe^y>$

a)

2x + 1

b)

2x - 1

c)

$2x+xe^y$

d)

$2x+1+xe^y$

9.

$\nabla\times\overrightarrow{F}$ is called

a)

0

b)

1

c)

Divergence

d)

Curl

10.

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

a)

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

b)

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

c)

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

d)

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

11.

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

a)

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

b)

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

c)

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

d)

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

12.

Find the gradient of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

13.

the derivative is...

a)

Gradient of the secant line

b)

Gradient of the tangent line

c)

Gradient of the cosecant line

d)

Gradient of the normal line

14.

The divergence at point P is...

a)

positive

b)

negative

c)

zero

15.

The vector field $\overrightarrow{F}\left(x,y,z\right)=<y^2,\ x^2e^z,\ \cos\left(xy\right)>$ is...

a)

conservative and incompressible.

b)

not conservative and incompressible

c)

conservative and not incompressible

d)

not conservative and not incompressible

16.

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

17.

The del operator is called as

a)

a) Gradient

b)

b) Curl

c)

c) Divergence

d)

d) Vector differential operator

18.

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

19.

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

20.

Laplacian of a potential V=x^2-y^2+z; at any point (1,1,1) is

a)

3

b)

2

c)

0

d)

-1

Vector Differentiation

Total questions: 20

Worksheet time: 3600secs

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