Chapter 11, Problem 6RE

To determine

To Find:Component form of the vector.

Answer to Problem 6RE

The required component of the vector is $\left(\frac{1}{2},\frac{1}{2}\right)$ .

Explanation of Solution

Given Information:

Since is unit vector the magnitude is $1$

Angle between vector and positive x-axis is $\frac{\pi }{6}$

Calculation:

Component form of the vector is

  $\begin{array}{l}a=\left|v\right|\cos \theta b=\left|v\right|\sin \theta \\ a=1\cos \frac{\pi }{6}b=1\sin \frac{\pi }{6}\\ a=\frac{1}{2}b=\frac{1}{2}\end{array}$

Conclusion:

Hence, the required component of the vector is $\left(\frac{1}{2},\frac{1}{2}\right)$ .