Chapter 14.2, Problem 3CE

To determine

Write a code to find out the magnitude and angle of the two vectors.

Answer to Problem 3CE

The solution is,

  

Explanation of Solution

Calculation:

Let’s take two vectors

  $\begin{array}{l}A=7i-6j\\ B=-15i+8j\end{array}$

Calculate the magnitude of both the vectors,

  $\begin{array}{l}x=7,x_1=-15\\ y=-15,y_1=8\end{array}$

  $\begin{array}{l}u=\sqrt{x^2+y^2}\\ v=\sqrt{x_1{}^2+y_2{}^2}\end{array}$

Then the resultant vector is,

  $R=u+v$

Then calculate the magnitude of the resultant vector,

  $m=\sqrt{R^2}$

Then the angle is,

  $angle=a\tan (R)$

Convert angle into degree by multiplying $\frac{180}{\pi }$ .

program:

clc
clear
close all
x=7;
y=-6;
u=sqrt(x.^2+y.^2);
x1=-15;
y1=8;
v=sqrt(x1.^2+y.^2);
R=u+v;
magnitude=sqrt(sum(R.*R));
angle=atan(R).*180/pi;
T=table(u,v,magnitude,angle)

Query:

• First, define the two vectors.
• Then calculate the magnitude of both the vectors.
• The calculate the resultant of the magnitudes.
• Find the angle and magnitude of the resultant vector.