Chapter 6.3, Problem 59E

To determine

Thecomponent form of v and sketch the specified vectoroperations geometrically.

Answer to Problem 59E

Thecomponent form of v is $v=\langle -2,-5\rangle$

Explanation of Solution

Given info:

  $\begin{array}{l}u=2i-j\text{ and }w=i+2j\\ v=u-2w\end{array}$

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 that

  $\begin{array}{l}v=u-2w\\ v=2i-j-2\left(i+2j\right)=-2i-5j\\ v=\langle -2,-5\rangle \end{array}$

The graph is given below

  

Conclusion:

Thus,thecomponent form of v is $v=\langle -2,-5\rangle$