We continue our study of vectors.

We can simplify the position of a point P on a plane by the vector OP where O is a reference point on the plane. The vector OP is called the position vector of P with respect to the reference point O. That is, every point on the plane can be represented by its position vector wrt the reference point O.

Then vector PQ = vector OQ – vector OP.

Furthermore, when we look at the coordinate plane for a point P (x, y), we can use its coordinates x and y to represent its position vector with respect to the origin O. We introduce column vector notation. A column vector is like a special form of a matrix (2 rows, 1 column). All matrix operations apply to column vectors.

We can apply what we have learned about vectors to help us solve geometry problems.

Notice when vector AB = vector DC, it means line AB is parallel to line DC and AB = DC.

Homework: Page 1, Page 2, Page 3, Page 4, Page 5, Page 6

Workbook Page 33: # 8, #9, #13, #19 – #26

Answers to last week’s homework: answers