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: Find the magnitude of the direction ratio vector:
\[ \sqrt{2^2+(-1)^2+(-2)^2}=\sqrt{4+1+4}=\sqrt9=3 \]

Step 2: Divide each ratio by the magnitude:
\[ \left(\dfrac23,\,-\dfrac13,\,-\dfrac23\right) \]

Final Answer:
\[ \boxed{\left(\dfrac23,-\dfrac13,-\dfrac23\right)} \]