Question

Find direction cosines of the line 6x-2=3y+1=2z-2.
Hence show l^2+m^2+n^2=1

Answer 1

First bring it to general form .

6x-2 = 3y + 1 = 2z-2

=> 6 ( x - 1/3 ) = 3 ( y -(-1) ) = 2 ( z - 1 )

divide all sides by lcm of 6 , 3 , 2 = 6

=> x -1/3 = (y -(-1) ) / 2 = ( z - 1 ) / 3

direction ratios are : 1 , 2 ,3
Magnitude= sqrt ( 1 + 4 + 9 ) = sqrt ( 14 )

now l,m,n = 1/sqrt 14 ,2/sqrt 14, 3/sqrt 14

so l^2 + m^2 + n^2 = ( 1 + 4 + 9 ) / 14 = 1 as always