RedCrab Math Tutorial


Vectors describe a direction and magnitude in a coordinate system. For calculations we use them as lists of numbers. But for understanding it can help to display them as geometric objects.
The vectorDefinition of a Vectorhas a magniutudeMagnitude of a Vector

Plot Vectors

To draw a vector, use a coordinate system. Draw a horizontal line and a line perpendicular. The horizontal line is the X-axis; the vertical line is the Y-axis. The axes labeled with numbers for the scales of the corresponding units.

The following figure shows the vector vector definitionorvector excample
  • The upper number is the x-coordinate and the lower the y-coordinate of the vector
To draw the vector (2, 3), move from its starting point 2 units on the x-axis to the right and 3 units on the y-axis to the top
Vector in coordinate system
The vector is uniquely defined by its direction and its length.

Equal Vectors

The following figure shows parallel vectors of equal length, direction and orientation. Since the location of a vector is arbitrary, these vectors are equal.
Equal Vectors Drawing

Opposite Vectors

Parallel vectors of equal length but opposite in orientation are called opposite vector

Opposite Vectors drawing

Parallel Vectors

Two vectors are called in parallel if they have the same direction. They can be different lengths and have opposite orientations.
draw parallel vectors

Vector Definition
Vector Calculation
Vector Addition
Vector Subtraction
Vector Magnitude
Vector Scalar Product
Angle between two Vectors

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