Give the cartesian coordinates of the point C… ˆ 4:4;  ˆ 1158; z ˆ 2†. (b)Give the cylindrical coordinates of the point D…x ˆ 3:1; y ˆ 2:6; z ˆ 3†. (c) Specifythe distance from C to D

(a) The Cartesian coordinates of point C are given in the problem as (4.4, -1158, 2).

(b) To convert the Cartesian coordinates of point D to cylindrical coordinates, we use the following formulas:

r = sqrt(x^2 + y^2) θ = atan(y/x) z = z

Substituting the given values:

r = sqrt((-3.1)^2 + 2.6^2) = sqrt(9.61 + 6.76) = sqrt(16.37) = 4.05 (approx) θ = atan(2.6/-3.1) = -39.8 degrees (approx) z = -3

So, the cylindrical coordinates of point D are (4.05, -39.8, -3).

(c) The distance from point C to point D in 3D space can be calculated using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Substituting the given values:

d = sqrt((4.4 - -3.1)^2 + (-1158 - 2.6)^2 + (2 - -3)^2) d = sqrt((7.5)^2 + (-1160.6)^2 + (5)^2) d = sqrt(56.25 + 1346683.36 + 25) d = sqrt(1346764.61) d = 1160.5 (approx)

So, the distance from point C to point D is approximately 1160.5 units.