Question

The projections of a directed line segment on the coordinate axes are $12,4\text{and}3.$ The direction cosines of the line are

• A. $(\frac{12}{13},\frac{-4}{13},\frac{3}{13})$
• B. $(\frac{-12}{13},\frac{-4}{13},\frac{3}{13})$
• C. $(\frac{12}{13},\frac{4}{13},\frac{3}{13})$
• D. $(\frac{12}{13},\frac{4}{13},\frac{-3}{13})$

Answer 1

The correct option is C $(\frac{12}{13},\frac{4}{13},\frac{3}{13})$

The projections on the coordinate axes are $12,4,3.$
Therefore, direction ratios are $12,4,3.$
Thus, the direction cosines of the line are $(\frac{12}{\sqrt{{12}^2+4^2+3^2}},\frac{4}{\sqrt{{12}^2+4^2+3^2}},\frac{3}{\sqrt{{12}^2+4^2+3^2}})$

$=(\frac{12}{13},\frac{4}{13},\frac{3}{13})$