Question

If the direction ratios of a line are (1, 1, 2), then find the direction cosines of the line.

• A. (1,1,2)
• B. $\left(0,\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)$
• C. $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}}\right)$
• D. $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)$

Answer 1

The correct option is C $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}}\right)$

The direction cosines are given by
$l=\frac{a}{\sqrt{a^2+b^2+c^2}},m=\frac{b}{\sqrt{a^2+b^2+c^2}},n=\frac{c}{\sqrt{a^2+b^2+c^2}}$
where (a, b, c) are direction ratios
Here a, b, c are 1, 1, 2 respectively.
Therefore,
$l=\frac{1}{\sqrt{1^2+1^2+2^2}},l=\frac{1}{\sqrt{6}}m=\frac{1}{\sqrt{1^2+1^2+2^2}},m=\frac{1}{\sqrt{6}}n=\frac{2}{\sqrt{1^2+1^2+2^2}},n=\frac{2}{\sqrt{6}}$
D.C.'s of the line are$\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}}\right)$