Geometric Vectors

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Geometric Vectors

• 8-1

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What is a vector?

• Suppose we are both traveling 65mph on Highway
  169 and we pass each other going opposite
  directions. Im heading back from Tulsa and you
  are heading to Tulsa. Describe our vectors.

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Vector Definition

• A quantity that has both a magnitude and a
  direction.

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Definition
A vector is defined to be a directed line
segment. It has both direction and magnitude
(distance). It may be named by a bold-faced
lower-case letter or by the two points forming
it - the initial point and the terminal point.
Examples u or AB u would be considered the
magnitude here.
B
u
A
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Look at the example on the board

• We have vector PQ, what is its magnitude?
• Absolute value bars are often used.

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Standard Position

• If a vector has an initial point at the origin,
  we consider it to be in standard position.
• The direction of a vector in standard position is
  given by the angle created between the positive
  x-axis and the vector
• Lets make a 115 degree vector r

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Zero Vector

• Draw the zero vector in standard position.

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Your turn

• Someone come up to the board and make a 4 inch 45
  degree vector.

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What would make two vectors equal?
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Your turn

• Draw two vectors that have the same magnitude but
  different directions.
• Draw to vectors that are equal.

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Can we sum vectors?

• What should we consider when summing a vector?

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2 Methods for Summing Vectors

• 1. Parallelogram Method
• 2. Triangle (Tip to Tail) method.
• We refer to the sums as resultant vectors

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Ok, lets add some vectors

• 1 student draw a vector
• 1 student draw another vector
• 1 student add the vectors

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What is an opposite vector?
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What are parallel vectors?
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Definition

• We often refer to the two vectors used for a sum
  of vectors as the components of the resultant
  vector For example

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Definition

• Scalar Quantity A quantity with only a
  magnitude.
• Give me some examples of scalar quantities.

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Lets practice some

• 14, 15, 16, 17, 21, 25, 31