Vectors (A-Level)
2D and 3D vectors; magnitude, scalar (dot) product, position vectors, parallel/perpendicular.
Y12: 2D. Y13: 3D and the dot product. a·b = |a||b|cosθ or component-wise a1b1 + a2b2 + a3b3. Perpendicular ⇔ dot product = 0.
Worked examples
a = (3i + 4j), |a| = 5.
a·b for a = (1, 2, 3), b = (4, 5, 6) = 4 + 10 + 18 = 32.
Angle between vectors: cosθ = a·b / (|a||b|).
Frequently asked questions
Position vector?
From origin to a point; OA = a says A has position vector a.
Vector equation of a line?
r = a + tb where a is a point on the line and b is a direction.