Chapter 6.3, Problem 35E

a.

To determine

To find: $u+v$ and sketch the resultant vector.

Answer to Problem 35E

  $u+v=\langle 1,-9\rangle$

Explanation of Solution

Given information:

The given vectorsare

  $u=\langle 0,-7\rangle$ , and $v=\langle 1,-2\rangle$ .

Calculation:

The addition of $u$ and $v$ is,

  $\begin{array}{c}u+v=\langle 0+1,-7+\left(-2\right)\rangle \\ =\langle 1,-7-2\rangle \\ =\langle 1,-9\rangle \end{array}$

The graph is as follows

  

b.

To determine

To find: $u-v$ and to sketch the resultant vector.

Answer to Problem 35E

  $u-v=\langle -1,-5\rangle$

Explanation of Solution

Calculation:

The subtraction of $u$ and $v$ is,

  $\begin{array}{c}u-v=\langle 0-1,-7-\left(-2\right)\rangle \\ =\langle -1,-7+2\rangle \\ =\langle -1,-5\rangle \end{array}$

The graph is as follows

  

c.

To determine

To find: $2u-3v$ and to sketch the resultant vector.

Answer to Problem 35E

  $2u-3v=\langle -3,-8\rangle$

Explanation of Solution

Calculation:

The difference of $2u$ and $3v$ is,

  $\begin{array}{c}2u-3v=2\langle 0,-7\rangle -3\langle 1,-2\rangle \\ =\langle 0,-14\rangle -\langle 3,-6\rangle \\ =\langle -3,-14+6\rangle \\ =\langle -3,-8\rangle \end{array}$

The graph is as follows