Simple explanation of Vectors
A vector is a quantity with magnitude (size/length) and direction. If two vectors have the same magnitude and direction, they're equal. Equal vectors are parallel.
Column Vectors
A column vector has an x-part (top) and a y-part (bottom).
- Positive x = right, negative x = left.
- Positive y = up, negative y= down.
Finding Column Vectors from Coordinates
- Method One: Plot the coordinates and find column vector by inspection.
- Method Two: Calculate. Find CD by D - C.
x: 5 - 6 = -1; y: 4 - -2 = 6 → CD
Comparing Column Vectors
E is at (3, -5). F is at (1, 7)
x: 1 - 3 = -2; y: 7 - -5 = 12
EF is twice as long as CD and parallel to it.
x: 1 - 3 = -2; y: 7 - -5 = 12
EF is twice as long as CD and parallel to it.
Parallel Vectors
Two vectors are parallel if one is a multiple of the other.
Opposite Vectors
Two vectors are opposite if their x and y values are the same but different signs.
Magnitude of a Vector
The magnitude of a vector is simply the length of the line. Use Pythagoras' Theorem to find the magnitude of a vector.
Angle to Horizontal
Use trigonometry (tan) to find the angle a vector makes to the horizontal (or vertical).
Adding Vectors
Just add the x-parts and y-parts separately. Similarly for subtracting.
Multiplying by a Number
Just multiply the x-parts and y-parts separately by the number.
Parallel to x- a y-axes
Vectors parallel to the x-axis include
i.e. the y-part is zero.
Vectors parallel to the y-axis include
i.e. the x-part is zero.
i.e. the y-part is zero.
Vectors parallel to the y-axis include
i.e. the x-part is zero.
