Chapter 6.1, Problem 9E

Solution

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

The component form of vector $2\overrightarrow{QS}$ is $\langle \left(-2,-24\right)\rangle$ .

The magnitude form of vector $\parallel 2\overrightarrow{QS}\parallel$ is $2\sqrt{145}$ .

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 $2\overrightarrow{QS}$ .

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:

  $Q=\left(3,4\right),S\left(2,-8\right)$

The component form of vector $\overrightarrow{QS}$ will be:

  $\begin{array}{l}\langle \left(2-3,-8-4\right)\rangle \\ =\langle \left(-1,-12\right)\rangle \end{array}$

The component form of $2\overrightarrow{QS}$ will be:

  $\begin{array}{l}2\langle \left(-1,-12\right)\rangle \\ =\langle \left(-2,-24\right)\rangle \end{array}$

The magnitude form of vector will be:

  $\begin{array}{l}\sqrt{{\left(-2\right)}^2+{\left(-24\right)}^2}\\ =\sqrt{4+576}\\ =\sqrt{580}\\ =2\sqrt{145}\end{array}$