Chapter 5, Problem 53A

To determine

To explain: The information thata , b and c represents.

Answer to Problem 53A

In the given equation, a and b are two vectors which are perpendicular to each other whilec is the resultant of these two vectors.

Explanation of Solution

Given:

By Pythagoras theorem,

  $c^2=a^2+b^2$

Formula used :

The resultant of two vectors is given as,

  $R=\sqrt{A^2+B^2+2AB\cos \theta }$

Here, A and B are two vectors which are inclined with each other at an angle $\theta$

Calculation:

Consider two vectors a and b that are perpendicular to each other as shown in figure below.

  

Figure 1 Now, let their resultant bec .

As a and b are perpendicular to each other so angle between them will be equal to $\theta =90°$ .

Therefore, resultant vector c will be

  $\begin{array}{l}c=\sqrt{a^2+b^2+2ab\cos 90°}\\ c=\sqrt{a^2+b^2+0}\\ c=\sqrt{a^2+b^2}\end{array}$

Now, squaring both side

  $c^2=a^2+b^2$

  

From the figure, it is clear that a and b are two vectors which are perpendicular to each other and c is the resultant of these two vectors.