Question

If the projections of the line segment $AB$ on the coordinate axes are $2,3,6$, then the sum of the d.cs of the line $AB$ is

• A. $11$
• B. $1$
• C. $\frac{11}{49}$
• D. $\frac{11}{7}$

Answer 1

The correct option is D $\frac{11}{7}$

Let $\overrightarrow{AB}=l\hat{i}+m\hat{j}+n\hat{k}$

Projection of $AB$ on $x,y,z$ axis are $l,m,n$ respectively

$\overrightarrow{AB}.\hat{i}=l=2$

$\overrightarrow{AB}.\hat{j}=m=3$

$\overrightarrow{AB}.\hat{k}=n=6$

$\overrightarrow{AB}=2\hat{i}+3\hat{j}+6\hat{k}$

$\left|\overrightarrow{AB}\right|=\sqrt{2^2+3^2+6^2}=7$

DR's of $\overrightarrow{AB}$ are $(2,3,6)$

DR's of $(\frac{2}{7},\frac{3}{7},\frac{6}{7})$

Sum of DR's $\frac{2+3+6}{7}=\frac{11}{7}$