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Homework 11

EECS 230 - Fall 2024

due: Wednesday, Oct. 2, 2024, Midnight

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1. (4pts, 1pt each) Convert from cartesian (x,y,z) to cylindrical coords (r,Φ,z)

(a) (1., 3., 6.)

(b) (12., 6., -5.)

(d) (-1., 2.5, -7.)

2. (4pts, 1pt each) Convert from cartesian (x,y,z) to spherical coords (R,θ‌,Φ).

(a) (3., 1., 2.)

(b) (11., 5., -20.)

(d) (-3., 2., 2.)

3. (4pts, 1pt each) Convert from cylindrical coords (r,Φ,z) to spherical coords (R,θ,Φ).

(a) (2., 0.13rad, 22.)

(b) (2.5, 166 o , -24.)

(d) (121., -0.35rad, -15.5)

4. (18pts) Given the range of coords, sketch (3pts) and determine the surface area (3pts).

(a) cartesian coords: x from 1. to 2.5, y from -10. to -5.

(b) cylindrical coords: r from 3. to 6, θ from 12 o to 35 o .

make your sketch at least 3inches by 3inches

5. (20pts, 10pts each) Given the following vector field:

and the cylindrical surface: r=3

Find: (a) the vector component of V normal to the surface

(b) the vector component of V tangential to the surface

6. (20pts, 10pts each) Given the following vector field:

and the spherical surface: R=6.5

Find: (a) the vector component of V normal to the surface

(b) the vector component of V tangential to the surface7. (30pts, 10 pts each) Given each of the vectors,

Find: (a) A vector perpendicular to it, in the same coordinate system (7pts).

(b) Verify using the dot product (3pts).

(a) cartesian: (3., -5, 12.)

(b) cylindrical: (21., 0.35rad, -12.)

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