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Vectors

A vector has MAGNITUDE and DIRECTION

 

Introduction to Geometric Vectors

A vector has MAGNITUDE and DIRECTION

Example:
30 miles south is a vector
The magnitude is 30 miles and the direction is south

A vector is represented by an ARROW
The LENGTH of the ARROW represent MAGNITUDE
The DIRECTION of the ARROW represents DIRECTION

 

 

Cartesian Vectors [may also called Algebraic Vectors]

A cartesian vector is expressed in terms of x and y components

Example:
In vector(3, 4)
the end point is 3 to the right of the start point
the end point is 4 higher than the start point

 

 

Finding The Magnitude Of A Cartesian Vector

[1] Square the x component of the vector
[2] Square the y component of the vector
[3] Add the squares of the x and y components
[4] Take the square root

Example:
vector(3, 4)
[1] 3 × 3 = 9
[2] 4 × 4 = 16
[3] 9 + 16 = 25
[4] √(25) = 5

Magnitude of vector(3, 4) = √(32 + 42)

 

 

Addition Of Cartesian Vectors

Add the x components of each vector together
Add the y components of each vector together

Example:
vector(1, 2) + vector(3, 4) = vector(1 + 3, 2 + 4) = vector(4, 6)

 

 

Unit Vectors

A unit vector has length one
A unit vector has magnitude one

Special unit vectors:
vector(1, 0)
vector(0, 1)

 

 

The Intersection Of Two Lines

QUESTION: What does it mean to say that lines are skew?
ANSWER: It means that the lines do NOT intersect

 

 

The Dot Product

Using The Scalar Product [Dot Product]
To Find The Angle Between Two Lines

 

 

 

 

 

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