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: Key Formula:
For direction ratios \(a,b,c\), the direction cosines are \(\dfrac{a}{\sqrt{a^2+b^2+c^2}},\dfrac{b}{\sqrt{a^2+b^2+c^2}},\dfrac{c}{\sqrt{a^2+b^2+c^2}}\).

Step 2: Computing the magnitude:
\(\sqrt{3^{2}+(-2)^{2}+(-6)^{2}}=\sqrt{9+4+36}=\sqrt{49}=7\).

Final Answer:
Direction cosines are \(\dfrac{3}{7},-\dfrac{2}{7},-\dfrac{6}{7}\).\[ \boxed{\left(\dfrac37,-\dfrac27,-\dfrac67\right)} \]