3-D Coordinates

3-D coordinates provide a crucial framework for pinpointing positions within three-dimensional space. They consist of three numerical values representing the x, y, and z axes, respectively, defining a point's location relative to a reference point or origin. This mathematical concept is fundamental in various fields, including computer graphics, engineering, physics, and geography. With 3-D coordinates, precise spatial relationships can be described, enabling accurate modeling, navigation, and analysis of complex systems and environments. Understanding 3-D coordinates facilitates the creation of immersive virtual worlds, the design of intricate structures, and the exploration of physical phenomena in three-dimensional space.

Questions
  • How do I convert from 3-D Cartesian coordinates to cylindrical coordinates?
  • How do I graph the point #(x, y, z) = (7, -5, 3)#?
  • What does it mean to say a 3-D coordinate system is right-handed?
  • What is meant by the 3-D Cartesian coordinate system?
  • What is meant by the cylindrical coordinates #(7, 30^circ, 9)#?
  • Let (x1,x2,x3) and (y1,y2,y3) represent the coordinates with respect to the bases B1={(1,0,0),(0,1,0),(0,0,1)},B2={(1,0,0),(0,1,2),(0,2,1)}.If Q(x)=x1²+2x1x2+2x2x3+x2²+x3²,find the representation if Q in terms of (y1,y2,y3).?
  • How to find x and y in terms of x' and y' respectively?
  • How to find the coordinates?
  • What is the 3-D Cartesian coordinate used for in real life?
  • What are the cartesian co-ordinates of r=2 ,angle=45?