Mathematics·Vectors and transformations · NSSCO 9.1
Vectors
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A vector is just an arrow that carries two pieces of news at once — how far, and in which direction. In this lesson we meet a vector as a directed line segment, write it neatly as a column vector (an x over a y), and learn the standard ways of writing it. Then we add and subtract vectors both by their columns and tip-to-tail on a grid, multiply a vector by a scalar, and measure its magnitude with Pythagoras. Finally we meet position vectors, find the vector joining two points with the rule b − a, hunt down midpoints, and learn to spot when two vectors are parallel.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 9.1):
- Understand a vector as a quantity with magnitude and direction, drawn as a directed line segment
- Write a vector as a column vector (x over y) and use the notations AB, a and |a|
- Describe a translation using a column vector
- Add and subtract vectors, both by their components and tip-to-tail on a grid
- Multiply a vector by a scalar and interpret it geometrically (parallel, scaled)
- Find the magnitude (modulus) of a vector using Pythagoras: |v| = √(x² + y²)
- Use position vectors, and find the vector joining two points as b − a
- Solve simple geometry problems with vectors: midpoints and parallel vectors
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