6.1 introduction to vectors · 6.1 introduction to vectors may 5 inc.notebook 1 may 04, 2016 6.1...
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6.1 Introduction to Vectors may 5 inc.notebook
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May 04, 2016
6.1 Introduction to VectorsScalars and Vectors
Scalars in mathematics and physics are quantities described completely or solely by a number and eventually a measurement unit. (Examples: Time, Length, Angles, Temperature,....)
Vectors are quantities described by both a "magnitude" (length, size) and a "direction".
Geometric and Algebraic Vectors
Geometric Vectors are NOT related to any coordinate system. (Just a picture of a line segment.
Consider the directed line segment
A
B
Note: where A is called the initial (start, tail) of the vector and B is the final (end, tip) of the vector.
Algebraic (Position) Vectors are vectors that ARE related to a coordinate system. (Cartesian Plane)
Given A(2,3), B(3,0), C(4,2)
Sketch
A)
B)
C)
6 5 4 3 2 1 0 1 2 3 4 5 6
6
5
4
3
2
1
1
2
3
4
5
6
x
y
Magnitude
The magnitude is the length, size, of the vector. The magnitude of a vector is denoted several different ways. The magnitude for vector is denoted by (Note: For geometric vectors the magnitude has to be given or measured. For algebraic vectors the magnitude can be calculated. (pythagorean theorem, sine cosine laws, etc)
6.1 Introduction to Vectors may 5 inc.notebook
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Sketch the following vectors on the grid and determine their magnitude
Given A(2,3), B(3,0), C(4,2)
5 4 3 2 1 0 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
x
y
A)
B)
C)
Equivalent or Equal Vectors
Two vectors are equal if they have the same magnitude and direction.
For example
A
B
C
D
Opposite (Negative) Vectors
Two vectors are called opposite if they have the same magnitude and opposite direction. The opposite vector of is denoted by .
Example:
A
B
C
D
6.1 Introduction to Vectors may 5 inc.notebook
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Parallel Vectors
Two vectors are parallel if their directions are either the same or the opposite. (Note: These vectors are NOT necessarily equal depending on their magnitude.)
If and are parallel, then we write
6.1 Introduction to Vectors may 5 inc.notebook
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Azimuth (Quadrant) Bearing
pg 279
1,411
6.1 Introduction to Vectors may 5 inc.notebook
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May 04, 2016