Question

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

Answer 1

The given direction ratios of a line are −18, 12 and −4.

Let the direction cosine of the line be l,m,n. Then direction cosines are,

l= a a 2 + b 2 + c 2 m= b a 2 + b 2 + c 2 n= c a 2 + b 2 + c 2

Here, a,b,c are the direction ratios of l,m,nrespectively.

Given, a=−18,b=12,c=−4.

a 2 + b 2 + c 2 = ( −18 ) 2 + 12 2 + ( −4 ) 2 = 324+144+16 = 484 =22

So, the direction cosines are,

l= −18 22 m= 12 22 n= −4 22

Thus, the direction cosines are −9 11 , 6 11 and −2 11 .