Question

Direction ratios of a line are 2, \(-1\) and \(-2\). Find the direction cosines of the line.

Hint:

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

Answer 1

Step 1: Recall direction cosines are the normalized direction ratios:
If $(a,b,c)$ are direction ratios, direction cosines are $(a,b,c)/\sqrt{a^2+b^2+c^2}$.

Step 2: Compute the normalizing factor:
$\sqrt{4+1+4}=3$.

Step 3: Scale each ratio:
$2/3,\ -1/3,\ -2/3$. Check: $(2/3)^2+(1/3)^2+(2/3)^2=4/9+1/9+4/9=1$ ✓.

Final Answer:
\[ \boxed{(2/3,\,-1/3,\,-2/3)} \]