Solve the following

Question:

A mosquito net over a $7 \mathrm{ft}^{\times} 4 \mathrm{ft}$ bed is $3 \mathrm{ft}$ high. The net has a hole at one corner of the bed through which a mosquito enters the bed. It flies and sits at the diagonally opposite upper corner of the net. (a) Find the magnitude of the displacement of the mosquito. (b) Taking the hole as the origin, the length of the bed as the X-axis, its width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.

 

Solution:

The displacement vector is given by $r=7 i+4 j+3 k$

Magnitude of displacement of the mosquitoes $=\left(7^{2}+4^{2}+3^{2}\right)^{1 / 2}=74 \mathrm{ft}$

The components of displacement along $x$ axis, $y$ axis and $z$ axis are 7 units, 4 units and 3 units respectively.

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