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Find the distance between two points A(5,60.,0) and B(10,90.,0) where the points are given in Cylindrical coordinates.

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Find the distance between two points A(5,60.,0) and B(10,90.,0) where the points are given in Cylindrical coordinates.

(a) 4.19 units

(b) 5.19 units

(c) 6.19 units

(d) 7.19 units

The question was asked at a job interview.

My question is from Conversion from Cartesian, Cylindrical and Spherical Coordinates topic in division Vector Differential Calculus of Engineering Mathematics

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Right choice is (c) 6.19 units

To elaborate: First convert each point which is in cylindrical coordinates to Cartesian coordinates. Now using the formula, distance \( = \sqrt{(x-x’)^2+(y-y’)^2 +(z-z’)^2} \), and substituting the values of x, y, and z in it, we get the required answer as 6.19 units. This sum can also be solved using a direct formula to find distance using two points in Cylindrical coordinates.

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