A mosquito net over a 7 ft × 4 ft bed is 3 ft high. The net has a hole at one corner of the bed through which a mosquito enters the net. 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, it width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.

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Solution

Displacement vector of the mosquito, $\vec{r} = 7 \hat{i} + 4 \hat{i} + 3 \hat{k}$

(a) Magnitude of displacement $= \sqrt{7^{2} + 4^{2} + 3^{2}}$
$= \sqrt{74} ft$

(b) The components of the displacement vector are 7 ft, 4 ft and 3 ft along the X, Y and Z-axes, respectively.

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