0

Guest

Courses New
Book a free demo of live class

Direction Ratios

 

If a, b, c are three numbers proportional to the direction cosine l, m, n of a straight line, then a, b, c are called its direction ratios. They are also called direction numbers or direction components.

Hence by definition, we have

1/a = m/b = n/c = k (say)

=> l = ak, m = bk, n = ck => k2(a2 + b2 + c2) = l2 + m2 + n2 = 1

=> k = ± 1 / √a2 + b2 + c2 = ± 1/√Σa2

 l = ± a/√Σa2.   Similarly m = ± b/√Σa2 and n = ± n/√Σa2

where the same sign either positive or negative is to be chosen throughout.

Example: If 2, – 3, 6 be the direction ratios, then the actual direction cosines are 2/7, –3/7, 6/7.

Note:

Direction cosines of a line are unique but direction ratios of a line in no way unique but can be infinite.

To read more, Buy study materials of 3D Geometry comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.


TOP Your EXAMS!

Upto 50% Scholarship on Live Classes

Course Features

  • Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Book a Live class Live courses Ask question
r