Question

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

What is the length of the line segment?

• A. $19units$
• B. $17units$
• C. $15units$
• D. $13units$

Answer 1

The correct option is D $13units$

Let the line segment be represented in the form of $\overrightarrow{a}=a_1\overrightarrow{i}+a_2\overrightarrow{j}+a_3\overrightarrow{k}$

Vector along coordinate axes are $\overrightarrow{i},\overrightarrow{j},\overrightarrow{k}$

Given that projection of $\overrightarrow{a}$ on x-axis is $12$, that with y-axis is $4$ and that with the z-axis is $3$

$\Rightarrow \overrightarrow{a}.\overrightarrow{i}=a_1=12$

Similarly $a_2=4,a_3=3$

$\therefore$ The length of the line segment is $\left|\overrightarrow{a}\right|=\sqrt{144+16+9}=13$ units.