The Vector Equation of a Line
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)?