Chapter 6.3, Problem 55E

To determine

Thecomponent form of v and sketch the specified vectoroperations geometrically.

Answer to Problem 55E

Thecomponent form of v is $v=\langle 3,-\frac{3}{2}\rangle$

Explanation of Solution

Given info:

  $\begin{array}{l}u=2i-j\text{ and }w=i+2j\\ v=\frac{3}{2}u\end{array}$

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

  $\begin{array}{l}v=\frac{3}{2}u\\ v=\frac{3}{2}\left(2i-j\right)=\frac{3}{2}\times 2i-\frac{3}{2}j=3i-\frac{3}{2}j\\ v=\langle 3,-\frac{3}{2}\rangle \end{array}$

The graph is given below

  

Conclusion:

Thus,thecomponent form of v is $v=\langle 3,-\frac{3}{2}\rangle$