Mr Kent's Lesson: 27 March, S2

Title: Vectors

Challenge Question

How can you prove two lines are parallel using vectors?

Learning Targets

Beginning

To be able to use vector notation to move between two points.

Developing

To be able to demonstrate how to describe the gap between any two points in terms of two or more vectors.

Mastering

To explain how to solve puzzles and prove facts using vectors.

Resources

Starter

Assess your understanding using this sorting exercise.

Vector Sorting Activity (print)

Beginning

Check you understanding

We are going to start by looking at using vector algebra to describe a movement from one point to another.

For example, in the questions below moving from A to B or C to D using the vectors p and q.

Note: A to B = p however if we go back the other way B to A = -p.

Vectors between to simple points (from MEP 19.3)*

Challenge Yourself
Vectors between simple points (open in Keynote)

Vectors Amber Treasure Hunt (print)

Developing

Check you understanding

We are now moving onto examples, where we are now dealing with just whole number vectors.
For example, in the questions below A to D = q however if you were to only move from A to a point half way along the line to D this would be the vector 0.5q.

Vectors between to any points (from MEP 19.3)*

Challenge Yourself

Vectors Green Treasure Hunt (print)

MangaHigh - Vectors between two points

Mastering

Check you understanding

Finally we are going to ask you to use your skills in using vectors to test (and there prove) some facts.

For example, you may be asked to check that two lines are parallel, one vector should be a multiple of the other.
Example 1: below O to R = 2r and P to Q = 2r these are clearly parallel as they are represented by the same vector.

Example 2: if one line is represented by 2a + 4b and a second by a + 2b we can see that the first vector is double the second. They are therefore parallel.

Proving facts using Vectors (from MEP 19.3)*