Chapter 6.3, Problem 44E

(a)

To determine

To calculate:

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

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Answer to Problem 44E

  $u+v=-i-4j$ andresultant’s graph of $-i-4j$ is

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Calculation:

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

  $\begin{array}{l}u+v=\left(-3+2\right)i+\left(1+\left(-5\right)\right)j\\ u+v=-i-4j\end{array}$

The resultant vector $u+v=-i-4j$ is graphed as below:

  

(b)

To determine

To calculate:

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

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Answer to Problem 44E

  $u-v=-5i+5j$ andresultant’s graph of $-5i+5j$ is

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Calculation:

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

  $\begin{array}{l}u-v=\left(-3-2\right)i+\left(1-\left(-5\right)\right)j\\ u-v=-5i+5j\end{array}$

The resultant vector $u-v=-5i+5j$ is graphed as below:

  

(c)

To determine

To calculate:

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

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Answer to Problem 44E

  $2u-3v=-12i+12j$ andresultant’s graph of $-12i+12j$ is

  

Explanation of Solution

Given information:

  $\begin{array}{l}u=\langle -3,1\rangle \\ v=\langle 2,-5\rangle \end{array}$

Calculation:

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

  $\begin{array}{l}2u=2\langle -3,1\rangle =\langle -6,2\rangle \\ 3v=3\langle 2,-5\rangle =\langle 6,-10\rangle \end{array}$

Now,

  $\begin{array}{l}2u-3v=\left(-6-6\right)i+\left(2-\left(-10\right)\right)j\\ 2u-3v=-12i+12j\end{array}$

The resultant vector $2u-3v=-12i+12j$ is graphed as below: