Unit 12 - Vectors

Unit Objectives
Prior Knowledge:
  • Vectors as movements in 2 dimensions
  • Sum, difference, scalar multiplication and magnitude of a vector 
By the end of this unit students should be able to:
  • Understand and use column and component forms of vectors in 2 and 3 dimensions
  • Know that  the vector AB is given by b - a
  • Calculate scalar products
  • Know and use the properties of the scalar product: commutative; distributive over addition; associative with scalar multiplication, scalar product of a vector with itself
  • Find the angle between two vectors (and lines) and identify parallel and perpendicular vectors
  • Understand and use the vector equation of a line
  • Convert to parametric and cartesian equations of lines
  • Solve problems of coincident, parallel, intersecting and skew lines
  • Identify points of intersection
  • Understand and use the definition of the vector product of two vectors
  • Know and use the properties of vector product:  non-commutative, distributive over addition,  associative with scalar multiplication, cross product of a vector with itself.
  • Interpret cross product geometrically
  • Understand and use the vector equation of a plane
  • Use the normal vector to convert between vector and Cartesian equations of planes
  • Find the intersection of: lines with planes, two planes, three planes
  • Find the angle between; a line and a plane, two planes
  • Identify if; unique, non-unique, no – solutions exist to systems of equations. Find solutions when they exist.
Lesson Resources​
1. Vectors Basics
2. Vectors in 3D
3. Vector Equations of a Straight Line
4. Scalar Products
5. Vector Product
6. Equation of Planes
7. Angles Between Lines and Planes
8. Distance to Lines and Planes
9. Intersection of Two Lines or Planes
10. Intersection of Three Planes
11. Modelling With Vectors
12. Vectors Review
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