Chapter 10.3, Problem 1QR

To determine

To find: The component form of the vector.

Answer to Problem 1QR

The components of the vector are $2\sqrt{3}$ and $2$ .

Explanation of Solution

Given information:

The magnitude and direction of a vector are $4$ and $30°$ , respectively.

Formula used:

Given the magnitude and direction of a vector $\overrightarrow{v}$ as $\left|v\right|$ and $\vartheta$ respectively, then the components of $\overrightarrow{v}$ in x and y direction are as follows:

  $\begin{array}{l}{v}_x=\left|v\right|\cos \theta \\ v_y=\left|v\right|\sin \theta \end{array}$

Calculation:

Calculate $v_x$ and $v_y$ .

  $\begin{array}{l}{v}_x=4\cos 30°=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}\\ v_y=4\sin 30°=4\times \frac{1}{2}=2\end{array}$

Therefore, the components of vector with magnitude $4$ and direction angle $30°$ are $2\sqrt{3}$ and $2$ , respectively.