Chapter 6.1, Problem 31E

Solution

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

The component form of vector is equal to $〈-14.52,44.70〉$ .

Given information:

Consider the given figure.

  

Concept used:

The component form of a vector is $\overrightarrow{a}=〈‖a‖\cos \theta ,‖a‖\sin \theta 〉$ .

Calculation:

Given,

  $\begin{array}{l}‖v‖=47\\ \theta ={108}^{\circ }\end{array}$ .

Apply the above concept and find the component form of the vector $\overrightarrow{v}$ below:

  $\begin{array}{c}\overrightarrow{v}=〈47\cos {108}^{\circ },47\sin {108}^{\circ }〉\\ =〈-14.52,44.70〉\end{array}$

Therefore, the component form of vector is $〈-14.52,44.70〉$ .