Free Printable Quiz on Vector Calculus

1.

A scalar has both magnitude and direction

a)

True

b)

False

2.

Vector A is defined in a rectangular coordinate system as being directed from P1[1,-2,2] to P2[-3,-4,6]. Determine the scalar component in the ax direction.

a)

-4

b)

4

c)

2

d)

-2

3.

Given the vectors

Find:

a)

4

b)

5

c)

6

d)

8

4.

Given the vectors find:

a)

$\frac{1}{3}a_x+\frac{1}{3}a_y+\frac{1}{3}a_z$

b)

$\frac{2}{3}a_x+\frac{1}{3}a_y+\frac{2}{3}a_z$

c)

$\frac{2}{3}a_x-\frac{2}{3}a_y+\frac{2}{3}a_z$

d)

$\frac{2}{3}a_x-\frac{1}{3}a_y+\frac{2}{3}a_z$

5.

Given the vectors: Find

a)

22ax + 8ay + 18az

b)

-22ax + 8ay + 18az

c)

-22ax - 8ay + 18az

d)

-22ax + 8ay - 18az

6.

Select the correct surface vector...

a)

dz ρdφ a_ρ

b)

dρ dz -a_φ

c)

dρ dz a_φ

d)

dρ ρdφ -a_z

e)

dρ ρdφ a_z

7.

Select the correct surface vector...

a)

dρ dz a_φ

b)

dρ ρdφ -a_z

c)

dρ ρdφ a_z

d)

dρ dz -a_φ

e)

dz ρdφ a_ρ

8.

Select the correct surface vector

a)

dρ ρdφ a_z

b)

dρ ρdφ -a_z

c)

dρ dz -a_φ

d)

dρ dz a_φ

e)

dz ρdφ a_ρ

9.

Please select the correct surface vector...

a)

r dθ dr a_ϕ

b)

- r dθ dr a_ϕ

c)

r sinθ dϕ dr a_θ

d)

r sinθ dϕ r dθ a_r

e)

- r sinθ dϕ dr a_θ

10.

Please select the correct surface vector...

a)

- r sinθ dϕ dr a_θ

b)

r sinθ dϕ r dθ a_r

c)

r sinθ dϕ dr a_θ

d)

- r dθ dr a_ϕ

e)

r sinθ dϕ r dθ dr a_r

11.

Please select the correct surface vector...

a)

r dθ dr a_ϕ

b)

r sinθ dϕ dr a_θ

c)

r sinθ dϕ r dθ a_r

d)

- r sinθ dϕ dr a_θ

e)

- r dθ dr a_ϕ

12.

The following describes a surface:

a)

True

b)

False

13.

Which of the following is not a surface?

a)

dρ ρdφ

b)

dρ dz

c)

dz ρdφ

d)

dz ρdφ dρ

14.

Which of the following is the surface in the aρ direction?

a)

dρ ρdφ

b)

dρ dz

c)

dz ρdφ

d)

dz ρdφ dρ

15.

Which of the following is the surface in the a_ϕ direction?

a)

d_ρ ρ dϕ

b)

d_ρ dz

c)

dz ρ dϕ

d)

dz ρ dϕ d_ρ

16.

Which of the following is the surface in the $a_{\theta}$ direction?

a)

rsinθ dϕ dr

b)

rdθ dr

c)

rsinθ dϕ

d)

rsinθ dϕ rdθ

17.

Determine the volume of a sphere

a)

4πplz

b)

4/3πr^2

c)

4/3πr^3

d)

none of the above

Quiz on Vector Calculus

Total questions: 17

Worksheet time: 28mins

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