Introduction to Vectors
Vectors represent quantities that have both magnitude and direction, and are fundamental tools in geometry, physics, and engineering.
What You Need to Know
Key Concept Diagram
A vector has both magnitude (size) and direction, unlike a scalar which has only magnitude
Vectors can be represented as directed line segments, component form (x, y), or column vectors
Vectors are added using the head-to-tail method or by adding corresponding components
The magnitude (length) of a vector v = (x, y) is |v| = √(x² + y²)
Key Vocabulary
Vector
A quantity with both magnitude and direction, represented by an arrow or component notation
Scalar
A quantity that has only magnitude (size) and no direction, such as temperature or speed
Resultant
The single vector that represents the sum of two or more vectors
Magnitude
The length or size of a vector, calculated using the distance formula
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Vector a = (3, 4). What is |a|, the magnitude of a?
Question 2
If a = (2, 3) and b = (−1, 4), what is a + b?
Question 3
Which of the following describes a scalar quantity?
Key Concepts Summary
- ●A vector has both magnitude (size) and direction, unlike a scalar which has only magnitude
- ●Vectors can be represented as directed line segments, component form (x, y), or column vectors
- ●Vectors are added using the head-to-tail method or by adding corresponding components
- ●The magnitude (length) of a vector v = (x, y) is |v| = √(x² + y²)