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### Vocabulary

##### Complete the chart.

Word | Definition |

Vector | ____________________________________________________________ |

____________ | the length of a line segment or vector |

Scalar | ____________________________________________________________ |

____________ | To move a vector on a coordinate system without changing its length or orientation |

### Multiply by a Scalar

A vector can be multiplied by a real number. This real number is called a _____________.

The product of a vector \begin{align*}\vec{a}\end{align*} and a scalar \begin{align*}k\end{align*} is a vector, written \begin{align*}\vec{ka}\end{align*} . It has the same direction as _____ with a magnitude of ________ if . If \begin{align*}k < 0\end{align*} , the vector has the opposite direction of _____ and a magnitude of ________ .

\begin{align*}\vec{i}\end{align*} is in standard position with terminal point (3, 7) and \begin{align*}\vec{j}\end{align*} is in standard position with terminal point (-2, 4).

- Find the coordinates of the terminal point of \begin{align*}5\vec{i} - \vec{j}\end{align*} .
- Find the coordinates of the terminal point of \begin{align*}0.2\vec{i} - 0.7\vec{j}\end{align*} .
- Find the coordinates of the terminal point of \begin{align*}8\vec{i} + 1.1\vec{j}\end{align*} .

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### Translate

Vectors with the same magnitude and direction are ____________. This means that the *same ordered pair* could represent *many different vectors*.

Think back: How do you find the slope of a line? _______________________

Are these two vectors equal?

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In each question below, the initial and terminal coordinates for a vector are given. If the vector is translated so that it is in standard position (with the initial point at the origin), what are the new terminal coordinates?

- initial (1, 6) and terminal (4, -2)
- initial (5, 3) and terminal (1, -6)
- initial (8, 4) and terminal (-9, 7)

Find the slope of each vector below with the given terminal coordinates. Assume the vector is in standard position.

- terminal (4, 9)
- terminal (7, 5)
- terminal (-3, 2)

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