Question

The projection of a directed line segment on the co-ordinate axes are $12,4,3$. Find the length and direction cosines.

Answer 1

Let the line,

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

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

ATQ : projection are given

$\overrightarrow{a}.\hat{i}=12,a_1=12$

$\overrightarrow{a}.\hat{j}=4,a_2=4$

$\overrightarrow{a}.\hat{k}=3,a_3=3$

Since,

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

length of the line segment $|\overrightarrow{a}|$

$=\sqrt{144+16+4}=13$