Question

The projections of a directed line segment on the coordinate axes $12,4,3$. 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. none of these

Answer 1

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

Assuming position vector of line segment ends point are $\overrightarrow{A}$ and $\overrightarrow{B}$
Now given projection of line segment on the axes are $(12,4,3)$
So $\overrightarrow{AB}=12\hat{i}+4\hat{j}+3\hat{k}$
Hence, direction cosine of line segment are $\frac{12}{\sqrt{{12}^2+4^2+3^2}},\frac{4}{\sqrt{{12}^2+4^2+3^2}},\frac{3}{\sqrt{{12}^2+4^2+3^2}}$ $\Rightarrow \frac{12}{13},\frac{4}{13},\frac{3}{13}$