Question

The projections of a directed line segment on the coordinate axes are $12,4,3$ respectively.

What are the direction cosines of the line segment?

• A. $(12/13,4/13,3/13)$
• B. $(12/13,-4/13,3/13)$
• C. $(12/13,-4/13,-3/13)$
• D. $(-12/13,-4/13,3/13)$

Answer 1

The correct option is A $(12/13,4/13,3/13)$

Let the direction cosines of the line segment in x,y,z are 12k, 4k, 3k respectively

But ${cos}^2\alpha +{cos}^2\beta +{cos}^2\gamma =1$

$\Rightarrow 144k^2+16k^2+9k^2=1\Rightarrow k^2=\frac{1}{169}\Rightarrow k=\frac{1}{13}$

$\therefore$ The direction cosines of the line segment are $(\frac{12}{13},\frac{4}{13},\frac{3}{13})$