1. Three Vectors A and B are given in a cylindrical Coordinate system As A=2ar +2aΦ+ az B=-ar+ 3aΦ-2az Compute:

1. Three Vectors A and B are given in a cylindrical Coordinate system As
A=2ar +2aΦ+ az
B=-ar+ 3aΦ-2az
Compute:
a. A+B
b. |A|
c. A.B
d. AxB
e. aB
f. A in cartesian coordinate system (Bonus)
2. Determine the gradient f(R,
3. Determine the curl F(y
4. Three Vector fields of A, B and C are given in a Cartesian Coordinate system as
A=2ax – az
B=2ax- ay+2az
C=2ax- 3ay+az
Determine:
a. (A+B).(A-B)
b. B.CXA
c. Compnent of A along B
d. Bonus; AX(BXC)
5. Determine the gradient f(r,
6. Two Vectors A and B are given in a Cartesian Coordinate system as
A=3ax +4ay+ az
B=2ay-5az
Compute:
a. A+B
b. A.B
c. AxB
d. aA
e. The angle between A and B
f. Determine B in Spherical coordinate system
7. Determine the gradient
a. f(r,
b. g(R, θ, Φ)=R sin2 θ
8. Bonus; Find the curl of, A=2x(ay)
9. Let V =xy2z3, evaluate and 2Vat point P(1,2,3)
10. Two Vectors A and B are given in a Cylindical Coordinate system as
A=3ar +2aΦ+ az
B=5ar -8az
Compute:
a. A+B
b. A.B
c. AxB
d. The angle between A and B
e. (Bonus) A in Cartesian coordinate system at P(2,π/2,-1)
11. Evaluate A(r,r Sin(ar+ r Cos(aΦ – raz
12. Vector A is given in a Cartesian Coordinate system as
A=24xyax +12(x2+2) ay+18z2 az Given at points, P(1,2,-1) and Q (-2,1,3),
Find;
a. A at P
b. |A| at P
c. A unit vector in the direction of A at Q
d. A unit vector directed from Q to P
e. The equation of the surface on which |A|=60
f. (Bonus) A in Cylindrical coordinate system at P
13. Determine the A(r,r2ar+r3aΦ+3rz2az
14. Evaluate the followings:
a. A= xy ax + y2 ay – xz az
b. B 10r Cos(Φ) – rz 2B
c. C= [ Sin (Φ)/R2] aR – [Cos(Φ)/ R2] aθ xC
15. Two Vectors A and B are given in a Cartesian Coordinate system as
A= 2ax – 6ay+3az
B= ax + 2ay – 2az
Compute:
a. A+B
b. A.B
c. AxB
d. The Element of A parallel with B
e. The angle between A and B
f. A in at P(2, 0, -1)
16. Evaluate;
a. for G(R,1/R2 Cos(θ)aR + RSin(Cos( Φ)aθ Cos(aΦ
b.