Unit 12 - Vectors - Mr R-C's Classes

Unit 12 - Vectors

Unit Objectives
Prior Knowledge:

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.