Chapter 6.3, Problem 41E

To determine

Toshow that $\frac{\text{a}}{b}=\frac{\text{c}}{\text{d}}$ then $\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}$

Answer to Problem 41E

After using the cross product property it is proved that $\frac{\text{a}}{b}=\frac{\text{c}}{\text{d}}$ then $\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}$

Explanation of Solution

Given information :

Consider the question $\frac{\text{a}}{b}=\frac{\text{c}}{\text{d}}$ then $\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}$

Calculations:

apply the cross products property to get the solution

Therefore,

The equation will be;

  $\begin{array}{l} \frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}\\ \text{ad = bc da = bc}\\ \text{now ad = da }\left[\text{commulative property}\right]\\ \therefore \text{ if }\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\text{ then }\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}\end{array}$

Therefore,After using the cross product property it is proved that $\frac{\text{a}}{b}=\frac{\text{c}}{\text{d}}$ then $\frac{\text{d}}{\text{c}}=\frac{\text{b}}{\text{a}}$