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The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates.
- a)True
- b)False
- c)Data can not be detemined
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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The Cartesian coordinates can be related to cylindrical coordinates an...
All the coordinate systems are inter-convertible and all the vector operations are applicable to it.
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The Cartesian coordinates can be related to cylindrical coordinates an...
Relation between Cartesian, Cylindrical, and Spherical Coordinates:
Cartesian Coordinates:
- Cartesian coordinates represent a point in space using X, Y, and Z coordinates.
- The X-axis represents the horizontal direction, the Y-axis represents the vertical direction, and the Z-axis represents the depth direction.
Cylindrical Coordinates:
- Cylindrical coordinates are represented in terms of distance from the origin, angle from the reference axis, and height from the XY plane.
- The conversion from Cartesian coordinates to cylindrical coordinates is given by:
- r = sqrt(x^2 + y^2)
- θ = arctan(y/x)
- z = z
Spherical Coordinates:
- Spherical coordinates are represented in terms of radial distance from the origin, azimuth angle from the reference axis, and polar angle from the Z-axis.
- The conversion from Cartesian coordinates to spherical coordinates is given by:
- ρ = sqrt(x^2 + y^2 + z^2)
- φ = arctan(sqrt(x^2 + y^2)/z)
- θ = arctan(y/x)
Relation between Cartesian, Cylindrical, and Spherical Coordinates:
- Cartesian coordinates, cylindrical coordinates, and spherical coordinates are related through mathematical transformations.
- By using appropriate formulas, a point in space represented in Cartesian coordinates can be converted to cylindrical or spherical coordinates, and vice versa.
- These coordinate systems provide different ways to represent the same point in space, offering flexibility in solving problems in various fields such as physics, engineering, and mathematics.
Cartesian Coordinates:
- Cartesian coordinates represent a point in space using X, Y, and Z coordinates.
- The X-axis represents the horizontal direction, the Y-axis represents the vertical direction, and the Z-axis represents the depth direction.
Cylindrical Coordinates:
- Cylindrical coordinates are represented in terms of distance from the origin, angle from the reference axis, and height from the XY plane.
- The conversion from Cartesian coordinates to cylindrical coordinates is given by:
- r = sqrt(x^2 + y^2)
- θ = arctan(y/x)
- z = z
Spherical Coordinates:
- Spherical coordinates are represented in terms of radial distance from the origin, azimuth angle from the reference axis, and polar angle from the Z-axis.
- The conversion from Cartesian coordinates to spherical coordinates is given by:
- ρ = sqrt(x^2 + y^2 + z^2)
- φ = arctan(sqrt(x^2 + y^2)/z)
- θ = arctan(y/x)
Relation between Cartesian, Cylindrical, and Spherical Coordinates:
- Cartesian coordinates, cylindrical coordinates, and spherical coordinates are related through mathematical transformations.
- By using appropriate formulas, a point in space represented in Cartesian coordinates can be converted to cylindrical or spherical coordinates, and vice versa.
- These coordinate systems provide different ways to represent the same point in space, offering flexibility in solving problems in various fields such as physics, engineering, and mathematics.
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The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates.a)Trueb)Falsec)Data can not be deteminedd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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