Chapter 6.3, Problem 120E

To determine

Write a program for a graphing utility that graphs two vectors and their difference given the vectors in the component form.

Explanation of Solution

Given: The two vectors and their difference.

The two vectors in the component form $u=<p,q>,v=<r,s>$ .The program sketches two vectors

  $u=pi+qj,v=ri+sj$ in the standard position , and then sketches the vectors difference $u-v$ using the parallelogram law .

The parallelogram law is used to find the difference between the vectors by addition of $u$ and $-v$ .

The program in graphing utility is coded as:

PROGRAM:

  $\begin{array}{l}\text{:Input "ENTER }P\text{",}P\\ \text{:Input "ENTER }Q\text{",}Q\\ \text{:Input "ENTER }R\text{",}R\\ \text{:Input "ENTER }S\text{",}S\\ \text{:Line (0,0,}P\text{,}Q\text{)}\\ \text{:Line (0,0,}R\text{,}S\text{)}\\ \text{:Pause}\\ \text{:}P-R\to E\\ :Q-S\to F\\ :\text{Line(}P,Q,R,S)\\ :\text{Line}(P,Q,E,F)\\ :\text{Line}(0,0,E,F)\\ :\text{Pause}\\ \text{:ClrDraw}\\ \text{:Stop}\end{array}$

The above program draws two vectors and their resultant by parallelogram law . This can be deduced by consideration of $u=<3,6>,v=<1,3>$

Here, $P=3,Q=6,R=1,S=3$