Two lines whose direction ratios are a_{1}, b_{1}, c_{1} and a_{2}, b_{2}, c_{2} are parallel, if
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The shortest distance between the lines whose equations are and is:
Two lines whose direction ratios are a_{1},b_{1},c_{1} and a_{2},b_{2},c_{2} are perpendicular, if
The shortest distance between the parallel lines whose equations are and
The angle between the lines x = 2y = – 3z and – 4x = 6y = – z is:
The angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0, 6nm  2nl + 5lm = 0 is:
209 videos443 docs143 tests

Example: Direction Cosines & Direction Ratios Video  10:24 min 
Test: Cartesian Equation Of A Line Test  10 ques 
Revision Notes: ThreeDimensional Geometry Doc  5 pages 
Direction Cosines and Direction Ratios of a Line Three Dimensional Geometry Video  03:22 min 
Test: Distance Formula 3D Geometry Test  10 ques 
209 videos443 docs143 tests

Example: Direction Cosines & Direction Ratios Video  10:24 min 
Test: Cartesian Equation Of A Line Test  10 ques 
Revision Notes: ThreeDimensional Geometry Doc  5 pages 
Direction Cosines and Direction Ratios of a Line Three Dimensional Geometry Video  03:22 min 
Test: Distance Formula 3D Geometry Test  10 ques 