Question

If the direction ratios of a line are \(3,-2,-6\), then find its direction cosines.

Hint:

Divide each direction ratio by the square root of the sum of their squares.

Answer 1

Step 1: Setting up the normalisation:
Direction cosines \(l,m,n\) must satisfy \(l^2+m^2+n^2=1\) and be proportional to \((3,-2,-6)\), so \(l=3k,m=-2k,n=-6k\).

Step 2: Solving for k:
\(9k^2+4k^2+36k^2=1\Rightarrow49k^2=1\Rightarrow k=\dfrac17\).

Final Answer:
\[ \boxed{\left(\dfrac37,-\dfrac27,-\dfrac67\right)} \]