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
