Question

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.

Answer 1

(a) The magnitude of the displacement of the mosquito is $\vec r = 7\vec i + 3\vec k + 4\vec i$

(b) The displacement vector has the components for 7 ft along the x-axis, 4 ft along the y-axis and 3 ft along the Z-axes.

Explanation:

The mosquito’s displacement vector is denoted as $\vec r = 7\vec i + 3\vec k + 4\vec i$

(a) The displacement’s magnitude = 72 + 32 + 42 = 74 ft

(b) The displacement vector has the components for 7 ft along the x-axis, 4 ft along the y-axis and 3 ft along the Z-axes.

It is to be observed that a vector is linked with various components and it is a mathematical entity. In other words, it can be said that it has a direction and a magnitude.