- 1. What Is a Vector?
Tell scalars from vectors, draw a vector as an arrow on a grid and write it as a column vector, use equal vectors to find unknowns, and write negative and zero vectors.
- 2. Adding and Subtracting Vectors
Add vectors head to tail and by the parallelogram law, subtract vectors as a + (-b), and find a vector by taking a different route round a triangle.
- 3. Scalar Multiples, Parallel and Collinear
Multiply a vector by a scalar, test whether vectors are parallel, show that three points are collinear and find the ratio of the lengths, and write one vector as m a + n b.
- 4. Position Vectors
Use position vectors and AB = OB - OA, move between column and i-j form, find midpoints, and find the point that divides a line in a given ratio.
- 5. Magnitude and Unit Vectors
Find the magnitude of a vector and the distance between two points, find unit vectors and direction cosines, find a vector of a given length in a given direction, and avoid the mistake |a + b| = |a| + |b|.
- 6. Direction: Angle, Components and Bearings
Turn a size and an angle into a column vector and back, handle every quadrant, and use WAEC's bearing form, where x = r sin(bearing) and y = r cos(bearing).
- 7. The Scalar (Dot) Product
Work out a dot product from components and from lengths and angle, find the angle between two vectors, and use a zero dot product to test for perpendicular vectors.
- 8. Capstone: Geometry with Vectors
Use position vectors, ratios, magnitudes and the dot product together to find the fourth vertex of a parallelogram, prove geometry facts, locate the centroid of a triangle, and find angles and areas.
