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# Vector Subtraction

## Negative vectors and the triangle method.

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Introduction to Vectors

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

1. Find the coordinates of the terminal point of the resultant vector.
2. What is the magnitude of the resultant vector?
3. 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).

1. Find the coordinates of the terminal point of \begin{align*}\vec{a} - \vec{b}\end{align*} .
2. What is the magnitude of \begin{align*}\vec{a} - \vec{b}\end{align*} ?
3. 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).

1. What is the ship's actual speed?
2. In what direction is the ship moving?
3. How far does the ship travel in 2 hours?
4. If the ship travels for 2 hours and then just floats for another two hours, how far has the trip traveled?
5. 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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