Question

The projection of a line segment on the axis of reference are 3, 4 and 12 respectively. The length of the line segment is

• A. $19$
• B. $\frac{19}{3}$
• C. $5$
• D. $13$

Answer 1

The correct option is D $13$

Given position vector of line

$\overrightarrow{a}=3\hat{i}+4\hat{j}+12\hat{k}$

length of line $=$ magnitude of $\overrightarrow{a}$

$\Rightarrow \left|\overrightarrow{a}\right|=\sqrt{3^2+4^2+{12}^2}$

$\Rightarrow \left|\overrightarrow{a}\right|=\sqrt{9+16+144}$

$\Rightarrow \left|\overrightarrow{a}\right|=\sqrt{169}$

$\Rightarrow \left|\overrightarrow{a}\right|=13$