Chapter 10.2, Problem 9E

(a)

To determine

To find: The component form of the vector $v$ .

Answer to Problem 9E

The component form of vector $v$ is $\langle 0,0,-4\rangle$ .

Explanation of Solution

Given information:

The given figure is:

  

Calculation:

Calculate the vector.

The component form of a vector $v$ having initial point $\left(p_1,p_2,p_3\right)$ and terminal point $\left(q_1,q_2,q_3\right)$ is given by

  $v=\langle q_1-p_1,q_2-p_2,q_3-p_3\rangle$

Consider the graph.

  

From the graph it can be said that the initial point of a vector $v$ is,

  $\left(p_1,p_2,p_3\right)=\left(2,0,1\right)$ .

The final point of the vector $v$ is,

  $\left(q_1,q_2,q_3\right)=\left(0,3,1\right)$ .

Thus the component form of a vector $v$ is,

  $\begin{array}{c}v=\langle q_1-p_1,q_2-p_2,q_3-p_3\rangle \\ =\langle 0-2,3-0,2-1\rangle \\ =\langle -2,3,1\rangle \end{array}$

Therefore, the component form of vector $v$ is $\langle -2,3,1\rangle$ .

(b)

To determine

To graph: The vector with the initial point at the origin.

Explanation of Solution

Given information:

The given initial points are $\left(p_1,p_2,p_3\right)=\left(2,0,1\right)$ , and the origin is $\left(-2,3,1\right)$ .

Graph:

Consider the vector with initial points at the origin.

  

Graph $\left(1\right)$

Interpretation:

The initial points are $\left(p_1,p_2,p_3\right)=\left(2,0,1\right)$ , and the origin $\left(-2,3,1\right)$ is shown in graph $\left(1\right)$ .