Chapter 10.2, Problem 8E

To determine

To find the component form of the vector $\text{v}$ .

Answer to Problem 8E

The component form of the vector $\text{v}=\langle -1,6,-8\rangle$ .

Explanation of Solution

Given information:

The initial and terminal points of the vector $\text{v}$ are $(1,-2,4)$ and $(0,4,-4)$ respectively.

Let, the initial point of the vector $\text{v}$$=\text{P(}{p}_1,p_2,p_3)=\text{P}(1,-2,4)$

and, the terminal point of the vector $\text{v}$$=\text{Q}(q_1,q_2,q_3)=\text{Q}(0,4,-4)$ .

So, the component form of the vector $\text{v}=\langle v_1,v_2,v_3\rangle$$=\langle q_1-p_1,q_2-p_2,q_3-p_3\rangle$ .

  $\begin{array}{l}\therefore v_1=0-1=-1\\ \therefore v_2=4-\left(-2\right)=4+2=6\\ \therefore v_3=-4-4=-8\end{array}$

Hence,

The component form of the vector $\text{v}=\langle -1,6,-8\rangle$ .