Chapter 6.2, Problem 5QR

Solution

To Find:

The component form of the vector $\overrightarrow{AB}$ .

  $〈3,\sqrt{3}〉$

Given:

  $A=\left(-2,0\right)$ and $B=\left(1,\sqrt{3}\right)$

Concepts Used:

For the points $A=\left(x_1,y_1\right)$ and $B=\left(x_2,y_2\right)$ , the vector $\overrightarrow{AB}$ represents the vector with initial point $A$ and terminal point $B$ . The vector $\overrightarrow{AB}$ is represented in component form as $〈x_2-x_1,y_2-y_1〉$ .

Calculations:

The component form of the vector $\overrightarrow{AB}$ for $A=\left(-2,0\right)$ and $B=\left(1,\sqrt{3}\right)$ :

  $\begin{array}{c}\overrightarrow{AB}=〈1-\left(-2\right),\sqrt{3}-0〉\\ =〈1+2,\sqrt{3}〉\\ =〈3,\sqrt{3}〉\end{array}$

Conclusion:

The component form of the vector $\overrightarrow{AB}$ is $〈3,\sqrt{3}〉$ .