Chapter 6.3, Problem 40E

(a)

To determine

To calculate:

The value of $u+v$ and the resultant’s graph for the following vectors

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Answer to Problem 40E

The resultant of given vectors is $u+v=6i+3j$

and it is graphed as below:

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Calculation:

The value of $u+v$ is calculated as:

  $\begin{array}{l}u+v=\left(2+4\right)i+\left(3+0\right)j\\ u+v=6i+3j\end{array}$

The resultant vector $u+v=6i+3j$

is graphed as below:

  

(b)

To determine

To calculate:

The value of $u-v$ and the resultant’s graph for the following vectors

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Answer to Problem 40E

The resultant of given vectors is $u-v=-2i+3j$

and it is graphed as below:

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Calculation:

The value of $u-v$ is calculated as:

  $\begin{array}{l}u-v=\left(2-4\right)i+\left(3-0\right)j\\ u-v=-2i+3j\end{array}$

The resultant vector $u-v=-2i+3j$

is graphed as below:

  

(c)

To determine

To calculate:

The value of $2u-3v$ and the resultant’s graph for the following vectors

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Answer to Problem 40E

The resultant of given vectors is $2u-3v=i-3j$

and it is graphed as below:

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle 2,3\rangle \\ v=\langle 4,0\rangle \end{array}$

Calculation:

The value of $2u-3v$ is calculated as:

  $\begin{array}{l}2u=2\langle 2,3\rangle =\langle 4,6\rangle \\ 3v=3\langle 1,3\rangle =\langle 3,9\rangle \end{array}$

Now,

  $\begin{array}{l}2u-3v=\left(4-3\right)i+\left(6-9\right)j\\ 2u-3v=i-3j\end{array}$

The resultant vector $2u-3v=i-3j$

is graphed as below: