Chapter 11, Problem 7RE

To determine

To Find:Component form of the vector.

Answer to Problem 7RE

The required component of the vector is $\frac{8}{\sqrt{17}}i-\frac{2}{\sqrt{17}}j$ .

Explanation of Solution

Given Information:

Given vector is $2\text{unit}$ long

Calculation:

Unit vector along $4i-j$ is $\frac{4i-j}{\sqrt{4^2+{\left(-1\right)}^2}}=\frac{4}{\sqrt{17}}i-\frac{1}{\sqrt{17}}j$

Since the vector is $2\text{unit}$ long therefore multiply $2$ with the vector.

  $\begin{array}{l}\frac{4}{\sqrt{17}}i-\frac{1}{\sqrt{17}}j\\ \frac{8}{\sqrt{17}}i-\frac{2}{\sqrt{17}}j\end{array}$

Conclusion:

Hence, the required component of the vector is $\frac{8}{\sqrt{17}}i-\frac{2}{\sqrt{17}}j$ .