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

Addition Of Geometric Vectors

Applications Of The Addition Of Geometric Vectors

Subtraction Of Geometric Vectors [0:00 - 3:41]

Addition And Subtraction Of Geometric Vectors

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)