Free Printable Coordinate Systems

1.

$A$

Determine component of vector $A⃗$

a)

$A⃗=3x̂-2ŷ-6ẑ$

b)

$A⃗=3x̂+2ŷ-6ẑ$

c)

$A⃗=-3x̂-2ŷ-6ẑ$

d)

$A⃗=3x̂+2ŷ+6ẑ$

2.

Identify $dl$ from A to B

a)

$x̂dx$

b)

$ŷdy$

c)

$ẑdz$

d)

$x̂dx+ŷdy$

3.

Identify the differential length,

dl

from A to B

a)

$dzẑ$

b)

$dyŷ$

c)

$dxx̂$

d)

$dyŷ+dzẑ$

4.

Identify dS for surface $1234$

a)

$x̂dydz$

b)

$ẑdxdy$

c)

$dxdydz$

d)

$x̂dx+ŷdy$

5.

Identify dS for surface $1234$

a)

$dxdyẑ$

b)

$dydzx̂$

c)

$dxx̂+dzẑ$

d)

$dxdzŷ$

6.

Find the vector A directed from (2,-4,1) to (0,-2,0) in cartesian coordinate.

a)

-2 $x̂$ +2 $ŷ$ - $ẑ$

b)

2 $x̂$ -2 $ŷ$ + $ẑ$

c)

-2 $x̂$ -2 $ŷ$ - $ẑ$

d)

2 $x̂$ -2 $ŷ$ - $ẑ$

7.

Which one is true to determine the surface for the shaded surface in Figure below:

a)

$x̂dydz$

b)

$ϕ̂drdz$

c)

$r̂rd\phi dz$

d)

$ẑrdrd\phi$

8.

Use the cylindrical coordinate system to find the area of the curved surface of a right circular cylinder where r=2m, $0≤\ z\ ≤5,\ 30°≤\ ϕ\ ≤120°$

a)

$3πm^2$

b)

$5πm^2$

c)

$πm^2$

d)

$2πm^2$

9.

Obtain the expression of a volume of a sphere from the differential volume. The range of sphere, $0≤R≤a$ $0°≤θ≤π$ and $0°≤ϕ≤2π$

$dV=R^2\sinθdRdθdϕ$

a)

$4\pi a^2$

b)

$4/3πa^3$

c)

$πa^2h$

d)

$πa^2$

10.

If vector B is given in the cylindrical form $E=r̂\cosϕ+ϕ̂\sinϕ$ , determine differential length, $dl_1$ component of Figure below and it's range.

a)

$r̂dr,\ r\ from\ 0\ to2$

b)

$ϕ̂rdϕ,\ ϕ\ from\ 0°\ to\ \ π$

c)

$ẑdz,\ z\ from\ 0\ to\ 2$

d)

$ϕ̂rdϕ,\ ϕ\ from\ π\ to\ 0$

Coordinate Systems

Total questions: 10

Worksheet time: 3600secs

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