Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 1,400 off
USE CODE: askschfd09

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.


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.

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 15,000 off
USE CODE: askschfd09