SHORTEST DISTANCE BETWEEN LINE

Theorem in Plane|| Theorem in Space|| Distance Between Point & a Line|| Distance Between Parallel Lines|| Shortest Distance Between Skew Lines

Statement 1: The shortest distance between the lines x/2=y/(-1)=z/2 and (x-1)/(-2)=(y-1)/-2=(z-1)/4 is sqrt(2) . Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line.

Statement 1: The shortest distance between the lines x/2=y/(-1)=z/2 and (x-1)/(4)=(y-1)/-2=(z-1)/4 is sqrt(2) . Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line.

Consider a hyperbola xy = 4 and a line y = 2x = 4 . O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is

Shortest distance between two parallel lines in vector + cartesian form

Shortest distance between two skew lines in vector + cartesian form

Show that the shortest distance between the lines x+a=2y=-12z and x=y+2a=6z-6a is 2a .