Introduction to Vectors
A vector is a mathematical quantity that has both magnitude (size) and direction, used to represent displacement, velocity, and force.
What You Need to Know
Key Concept Diagram
A vector in 2D is written as a column matrix or in component form (x, y)
Vectors can be added head-to-tail or by adding corresponding components
The magnitude (length) of vector (a, b) is √(a² + b²)
The dot product of two vectors detects whether they are perpendicular (dot product = 0)
Key Vocabulary
Vector
A quantity with both magnitude and direction, often represented as an arrow or column matrix
Magnitude
The length or size of a vector, calculated using the Pythagorean theorem from its components
Unit Vector
A vector with magnitude equal to 1, used to indicate direction only
Dot Product
The scalar result of multiplying corresponding components of two vectors and summing: a·b = a₁b₁ + a₂b₂
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the magnitude of the vector (3, 4)?
Question 2
If vectors a = (2, 3) and b = (1, 5), what is a + b?
Question 3
Two vectors have a dot product of 0. What can be concluded?
Key Concepts Summary
- ●A vector in 2D is written as a column matrix or in component form (x, y)
- ●Vectors can be added head-to-tail or by adding corresponding components
- ●The magnitude (length) of vector (a, b) is √(a² + b²)
- ●The dot product of two vectors detects whether they are perpendicular (dot product = 0)