We go over the application of vectors, particularly in geometry.

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

If you have not done your homework last week because you have some questions on certain problems, please do them now:

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

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

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 homework: answers

For a given vector a, a vector which has the same magnitude but in the opposite direction of a is called the negative of vector a , and is denoted by –a.

The subtraction of a vector v from a vector u can be denoted as adding the vector –v to u: u – v = u + (-v).

A vector with the same initial point and the terminal point has zero magnitude. It is called a zero vector, or a null vector, and is denoted by 0. a + (-a) = a  – a = 0.

When a vector a is multiplied by a constant k, the product ka is called a scalar multiplication of a and is defined as follows:

* If k > 0, ka is a vector with magnitude k|a| and in the same direction as a;

* If k < 0, ka is a vector with magnitude -k|a| and in the opposite direction of a;

* If k = 0, ka is a zero vector 0.

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

Workbook Page 33, #6, #7, #10, #11, #14 – #18, #20, #21.