Chapter 6.1, Problem 8E

Solution

To find: The component form and magnitude of the vector.

The component form of vector $\overrightarrow{PS}$ is $\langle 4,-10\rangle$ .

The magnitude form of vector $\parallel \overrightarrow{PS}\parallel$ is $4\sqrt{7}$ .

Given information:

Let $P=\left(-2,2\right),Q\left(3,4\right),R\left(-2,5\right)$ and $S\left(2,-8\right)$ . Find the component form and magnitude of the vector.

Find $\overrightarrow{PS}$ .

Concept used:

Let the initial side of the vector is $\left(x_1,y_1\right)$ and the terminal side of the vector be $\left(x_2,y_2\right)$ .

Then, the component form of the vector will be:

  $\langle \left(x_2-x_1,y_2-y_1\right)\rangle \text{or }\langle x,y\rangle$

The magnitude form of the vector will be:

  $\sqrt{x^2+y^2}$

Explanation:

  $P=\left(-2,2\right),R\left(2,-8\right)$

The component form of vector will be:

  $\begin{array}{l}\langle 2-\left(-2\right),-8-2\rangle \\ =\langle 2+2,-10\rangle \\ =\langle 4,-10\rangle \end{array}$

The magnitude form of vector will be:

  $\begin{array}{l}\sqrt{4^2+{\left(-10\right)}^2}\\ =\sqrt{16+100}\\ =\sqrt{116}\\ =4\sqrt{7}\end{array}$