2. 1
1. Given point P(—2, 6, 3) and vector A = yax + (x + z)ay, express P and A in cylindrical and
spherical coordinates. Evaluate A at P in the Cartesian, cylindrical, and spherical systems
2. Convert points P(1, 3, 5), T(0 - 4 , 3), and S(-3, - 4 , -10) from Cartesian to cylindrical and
spherical coordinates.
3. Transform vector
Q =
√
x2+y2ax
√
x2+y2+z2
− yzaz
√
x2+y2+z2
to cylindrical and spherical coordinates and Evaluate Q at T in the three coordinate systems.
1. Express vector
B=10
r ar + rcosθaθ + aφ
in Cartesian and cylindrical coordinates. Find B(−3, 4, 0)andB(5, π/2, −2).
2.Express the following vectors in Cartesian coordinates:
A. ρzsinφaρ + 3ρcosφaφ + ρcosφsinφaz
B.r2
ar + sinθaφ
