Question

The projection of a line segment on the axes are $3,4,12$ then the length of the lie segment is

• A. $19$
• B. $19/3$
• C. $5$
• D. $13$

Answer 1

The correct option is D $13$

We have,

projection $\overrightarrow{a}$ and $\overrightarrow{b}$

$=\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{|\overrightarrow{b}|}$

$\therefore \overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$

$a_1\hat{i}\hat{j}=a_1$

$a_1=12$

$a\hat{i}\hat{j}=a_2$

$a_2=4$

$\therefore a_3=3$

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

$|\overrightarrow{a}|=\sqrt{(12{)}^2+(4{)}^2+(3{)}^2}$

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

$|\overrightarrow{a}|=\sqrt{169}$

$|\overrightarrow{a}|=13$

Hence, this is answer.