A bird moves in such a way that it has a displacement of 12 m towards east, 5 m towards north and 9 m vertically upwards. Find the magnitude of its displacement.

$\sqrt{{12}^2+5^2}=13$

Vertically up, So it is perpendicular to ‘R’

$=\sqrt{{13}^2+9^2}=\text{S}$

$\text{S}=\sqrt{250}$

$\text{S}=\sqrt{25\times 10}=5\sqrt{10}$

(or)

Alternate method : -

$\overrightarrow{S}=12\hat{i}+5\hat{j}+9\hat{k}$

$\left|S\right|=\sqrt{{12}^2+5^2+9^2}$

$=\sqrt{144+25+81}$

$=\sqrt{250}=5\sqrt{10}$