Chapter 11.3, Problem 1QR

To determine

To find: Thecomponents of a vector with magnitude 4 and direction angle $30°$

Answer to Problem 1QR

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

Explanation of Solution

Given information:

Magnitude = 4

Direction angle = $30°$

Formula used:

Components of a vector with magnitude $m$ and direction angle $\theta$ :

  $m\sin \theta \text{and}m\cos \theta$

Calculation:

Given that the magnitude of the vector is 4 and the direction angle $30°$ .

Now, calculate the components of the vector.

Substitute $m=4$ and $\theta =30°$ in the expression $m\sin \theta$ .

Thus, the sin component is

  $\begin{array}{c}m\sin \theta =4\sin 30°\\ =4\times \frac{1}{2}\\ =2\end{array}$

Similarly, the cosine component. Use the expression $m\cos \theta$

  $\begin{array}{c}m\cos \theta =4\cos 30°\\ =4\times \frac{\sqrt{3}}{2}\\ =2\sqrt{3}\end{array}$

Conclusion:

Hence, the required components of the vector are $2\text{and}2\sqrt{3}$ .