Straight Line in 3D

Straight Line in 3D P(x, y, z) & Q(x, y, z) are two points given is space. X, Y & Z axes are drawn. θ represents rotation of system about Y axis from X to Z. α represents rotation of of system about X axis from Y to Z. So if θ = α = 0 one sees X & Y ⊥ to each other and Z as a point. If θ = 90° and α = 0 then X & Z axes are seen with Y as point. If θ = 0 & α = 90° then one sees X & Z axes. A slider L is provided to change lengths of axes. A rectangular parallelepiped is constructed with P & Q as opposite vertexes. So PCFE & QBAD are faces ⊥ to X axis. large number of problems may be tackled by choice of n by a slider. α & θ are changed by sliders. This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com An array of coordinates Cor of set of points P & Q is written with 1st 3 columns for P & next 3 for Q. Axes tips and vertexes of rectangular parallelepiped are now defined in 3D as X3D, Y3D, P3D etc,  All Points are transformed to 2D coordinated    x = X cos(θ) - Z sin(θ) & y = Y cos(α) - Z sin(α) cos(θ) - X sin(α) sin(θ) These points are plotted and joined by relevant segments. Some faces are shown as colored polygons.   Required distances are calculated by    dPQ = sqrt[ (xQ - xP)² + (yQ - yP)² + (zQ - zP)² ] Dr Vasant Barve, 10 August 2014, Created with GeoGebra