This investigation looks at the vector equation of a line. The construction is defined by some key points.
The line passing through points A and R is parallel to vector b.
The points A and R are fixed to the line.

Thinking critically about your previous knowledge of vectors, explore the following applet by moving around points R, A, and the end points of b whilst observing the the information given in the algebra view.
Answer the following questions.
1. What is the algebraic relationship between vector b and vector AR?
2. Can you define the vector r in terms of the vector a and the vector AR?
3. What does a represent in general terms?
4. What comparisons can you make between your answer to question 2 and the equation for a line (y=mx + c)?