Conversion to cylindrical co-ordinates

[sfunds]

Conversion to cylindrical co-ordinates...please help

I came a across the following problem in William Hayt book.

1.) Expresss in cylindrical componenets:(a) vector from C ( 3,2,-7) to D (-1,-4,2)

The following is the solution in the solution manual of that book:
a) the vector from C(3, 2,−7) to D(−1,−4, 2):
C(3, 2,−7) → C(ρ = 3.61, φ = 33.7◦, z = −7) and
D(−1,−4, 2) → D(ρ = 4.12, φ = −104.0◦, z = 2).
Now RCD = (−4,−6, 9) and Rρ = RCD · aρ = −4 cos(33.7) − 6 sin(33.7) = −6.66. Then
Rφ = RCD · aφ = 4 sin(33.7) − 6 cos(33.7) = −2.77. So RCD = −6.66aρ − 2.77aφ + 9az

why have they taken angle 33.7 to find RCD ??

I don't understand

 

[lippyka]

the answer given in the solution manual. The conversion of the vector C to cylindrical components is straightforward, so why have they considered the angle 33.7°?The solution manual has taken the angle 33.7° in order to calculate the components of the vector from C to D in cylindrical coordinates. The angle 33.7° is the angle between the vector from C to D and the x-axis in the xy-plane. By using this angle, the authors were able to calculate the components of the vector in cylindrical coordinates.