Question

The projections of a line segment on the coordinates axes are $2,3,6$. Then the length of the line segment is

• A. $7$
• B. $5$
• C. $1$
• D. $11$

Answer 1

The correct option is A $7$

Let position vector of line segment ends point are $\overrightarrow{A}$ and $\overrightarrow{B}$

Now given projection of line segment on the axes are $(2,3,6)$

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

Hence, length of line segment $=\mid \overrightarrow{AB}\mid =\sqrt{2^2+3^2+6^2}=7$