Chapter 6, Problem 9CT

To determine

The component form of the vector v satisfying the givenconditions.

Answer to Problem 9CT

Thecomponent form of v is $v=\langle 14,-23\rangle$

Explanation of Solution

Given info:

Initial point of $v:(-3,7);$ terminal point of $v:(11,-16);$

Formula used:

A vector whose initial point is the origin $(0,0)$ can be uniquely represented by thecoordinates of its terminal point $(v_1,v_2)$ . This is the component form of a vector v,written as $v=\langle v_1,v_2\rangle$

Calculation:

Given thatinitial point of $v:(-3,7);$ terminal point of $v:(11,-16);$

  $\begin{array}{l}v=\langle v_1,v_2\rangle \\ v_1=11-\left(-3\right)=14\\ v_2=-16-7=-23\\ v=\langle 14,-23\rangle \end{array}$

Conclusion:

Thus,thecomponent form of v is $v=\langle 14,-23\rangle$