Coordinate Systems

 $A$  

Determine component of vector  $A⃗$  

•  $A⃗=3x̂-2ŷ-6ẑ$  

•  $A⃗=3x̂+2ŷ-6ẑ$  

•  $A⃗=-3x̂-2ŷ-6ẑ$  

•  $A⃗=3x̂+2ŷ+6ẑ$  

 Identify  $dl$  from A to B

•  $x̂dx$  

•  $ŷdy$  

•  $ẑdz$  

•  $x̂dx+ŷdy$  

Identify the differential length,  $dl$  from A to B

•  $dzẑ$  

•  $dyŷ$  

•  $dxx̂$  

•  $dyŷ+dzẑ$  

Identify dS for surface  $1234$  

•  $x̂dydz$  

•  $ẑdxdy$  

•  $dxdydz$  

•  $x̂dx+ŷdy$  

Identify dS for surface  $1234$  

•  $dxdyẑ$  

•  $dydzx̂$  

•  $dxx̂+dzẑ$  

•  $dxdzŷ$  

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

• -2 $x̂$  +2 $ŷ$ - $ẑ$   

• 2 $x̂$  -2 $ŷ$ + $ẑ$   

• -2 $x̂$  -2 $ŷ$ - $ẑ$   

• 2 $x̂$  -2 $ŷ$ - $ẑ$   

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

• $x̂dydz$

• $ϕ̂drdz$

• $r̂rd\phi dz$

• $ẑrdrd\phi$

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

•  $3πm^2$  

•  $5πm^2$  

•  $πm^2$  

•  $2πm^2$  

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

 $dV=R^2\sinθdRdθdϕ$  

•  $4\pi a^2$  

•  $4/3πa^3$  

•  $πa^2h$  

•  $πa^2$  

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.

•  $r̂dr,\ r\ from\ 0\ to2$  

•  $ϕ̂rdϕ,\ ϕ\ from\ 0°\ to\ \ π$  

•  $ẑdz,\ z\ from\ 0\ to\ 2$  

•  $ϕ̂rdϕ,\ ϕ\ from\ π\ to\ 0$