Question

If the projections of the line segment $\underset{PQ}{\to }$ on the axes are 3,4,12 then the length of $\underset{PQ}{\to }$ is

Answer 1

Length of $\overrightarrow{PQ}=\sqrt{3^2+4^2+{12}^2}$

$=\sqrt{5^2+{12}^2}$

$=\sqrt{{13}^2}$

$=13$

$($since, projection of $\overrightarrow{PQ}$ on x-axis is $|\overrightarrow{PQ}|=\cos \alpha =3$

projection of $\overrightarrow{PQ}$ on y-axis is $|\overrightarrow{PQ}|\cos \beta =4$

projection of $\overrightarrow{PQ}$ on z-axis is $|\overrightarrow{PQ}|\cos \gamma =12$

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1)$.