Relation between vector length and direction ratios

[Krushnaraj Pandya]

Homework Statement

A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by?

Homework Equations

l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios
l^2 + m^2 + n^2=1...(2)

The Attempt at a Solution

putting values in (1) gives us l/2 = m/-3 = n/6, using 2 we get modulus of l=2/7. Since the angle is obtuse l will be negative = -2/7 and therefore m and n are equal to 3/7 and -6/7 which is correct- Why is the information that r has length 21 given then? and how does our answer match with the length being 21?

 

[LCKurtz]

If all you want is the direction cosines, the length is indeed irrelevant.

 

[phinds]

I can't see that the length is relevant to the problem. Sometimes problem statements have extraneous information.

EDIT: I see that LCKurtz beat me to it.

 

[Krushnaraj Pandya]

If all you want is the direction cosines, the length is indeed irrelevant.

I can't see that the length is relevant to the problem. Sometimes problem statements have extraneous information.

EDIT: I see that LCKurtz beat me to it.

Thank you very much for your help :D