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### Vocabulary

##### Complete the chart.

Word | Definition |

_____________ | a type of mathematical quantity that has both a magnitude and a direction |

_____________ | a portion of a line that has both a magnitude and direction. |

Magnitude | _________________________________________________________________ |

Parallelogram Method | _________________________________________________________________ |

_____________ | a vector representing the sum of two or more vectors |

Triangle Method | _________________________________________________________________ |

_____________ | a vector that is the same in magnitude as the original vector, but opposite in direction |

Displacement | _________________________________________________________________ |

### Vectors

A vector is said to be in **standard position **if its _____________________ is at the origin. The initial point is where the vector ____________ and the ____________________ is where it ends.

How do we find the **magnitude** of a vector? _________________________________

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- How can you determine the direction of a vector if you know its initial point and terminal point?
- How can you determine whether or not two vectors are equal?
- If a vector starts at the origin and has a terminal point with coordinates (3, 9), find the magnitude of the vector.
- If a vector has an initial point at (1, 4) and has a terminal point at (6, 13), find the magnitude of the vector.

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#### Vector Addition

In your own words, describe how to use the Parallelogram Method to find the resultant when adding two vectors. _____________________________________________________________________

Also describe how to use the Triangle Method to find the resultant when adding two vectors. _____________________________________________________________________

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\begin{align*}\vec{a}\end{align*} is in standard position with terminal point (1, 5) and \begin{align*}\vec{b}\end{align*} is in standard position with terminal point (7, 4).

- Find the coordinates of the terminal point of the resultant vector.
- What is the magnitude of the resultant vector?
- What is the direction of the resultant vector?

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#### Vector Subtraction

When we think of vector subtraction, we must think about it in terms of adding a __________________. You can use the same methods as vector addition.

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\begin{align*}\vec{a}\end{align*} is in standard position with terminal point (6, 3) and \begin{align*}\vec{b}\end{align*} is in standard position with terminal point (9, 4).

- Find the coordinates of the terminal point of \begin{align*}\vec{a} - \vec{b}\end{align*} .
- What is the magnitude of \begin{align*}\vec{a} - \vec{b}\end{align*} ?
- What is the direction of \begin{align*}\vec{a} - \vec{b}\end{align*} ?

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#### Resultant of Two Displacements

We can use vectors to find ______________, ______________, and ______________ of moving objects.

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A ship is traveling north at 45 mph. A constant 5 mph wind is coming from the east (blowing west).

- What is the ship's actual speed?
- In what direction is the ship moving?
- How far does the ship travel in 2 hours?
- If the ship travels for 2 hours and then just floats for another two hours, how far has the trip traveled?
- If the ship travels for 2 hours and then just floats for another two hours, how far from its starting point is the ship?

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