Magnitude of a 2 dimensional vector

Magnitude of a 2 dimensional vector

Introduction to Magnitude of a 2D Vector

• A 2D Vector is represented by an ordered pair of numbers such as (x, y) where ‘x’ describes the horizontal displacement and ‘y’ describes the vertical displacement.
• The magnitude of a vector refers to its length or size.
• In the context of a 2D vector, magnitude gives the straight-line distance from the origin (0,0) to the point represented by the vector.

Calculating the Magnitude

• The magnitude of a 2D vector (x, y) is calculated using the Pythagorean theorem.
• The formula for deriving the magnitude of a vector is sqrt(x² + y²).
• Here sqrt refers to the square root, ‘x’ is the displacement in the x-direction (horizontal), and ‘y’ is the displacement in the y-direction (vertical).
• For instance, the magnitude of a vector (3,4) is sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25) = 5.

Properties of Magnitude

• The magnitude of any vector is always a non-negative number (0 or positive).
• The magnitude is only zero when the vector is the zero vector, represented as (0,0).

Practical Applications

• The concept of magnitude is prevalent in various scientific disciplines including physics, engineering and computer science.
• In particular, it’s used to describe quantities such as velocity, force, and displacement.

Revision Tips

• Practice calculating the magnitude of 2D vectors with different x and y values.
• Familiarise yourself with the Pythagorean theorem and its application in computing vector magnitudes.
• Challenge yourself by applying the concept of magnitude to solve real-world mathematical problems.