Chapter 11.2, Problem 17E

(a)

To determine

To sketch: The given vector.

Explanation of Solution

Given information:

The given vector is,

  $v=2i+2j-k$

The value of the vector $z$ is calculated as,

  $\begin{array}{c}z=2v\\ =2\langle 2,2,-1\rangle \\ =\langle 4,4,-2\rangle \end{array}$

Consider the sketch of the given vector,

  

(b)

To determine

To sketch: The given vector.

Explanation of Solution

Given information:

The given vector is,

  $v=2i+2j-k$

The value of the vector $z$ is calculated as,

  $\begin{array}{c}z=-v\\ =-\langle 2,2,-1\rangle \\ =\langle -2,-2,1\rangle \end{array}$

Consider the sketch of the given vector,

  

(c)

To determine

To sketch: The given vector.

Explanation of Solution

Given information:

The given vector is,

  $v=2i+2j-k$

The value of the vector $z$ is calculated as,

  $\begin{array}{c}z=\frac{5}{2}v\\ =\frac{5}{2}\langle 2,2,-1\rangle \\ =\langle 5,5,-\frac{5}{2}\rangle \end{array}$

Consider the sketch of the given vector,

  

(d)

To determine

To sketch: The given vector.

Explanation of Solution

Given information:

The given vector is,

  $v=2i+2j-k$

The value of the vector $z$ is calculated as,

  $\begin{array}{c}z=0v\\ =0\langle 2,2,-1\rangle \\ =\langle 0,0,0\rangle \end{array}$

Consider the sketch of the given vector,