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:

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

We start the new chapter on vectors.

While a scalor is a quantity that has only magnitude, a vector is a quantity that has both magnitude and direction. We usually use directed line segment to represent a vector. The direction of the line segment, indicated by an arrow, represents the direction of the vector, and the length of the line segment represents the magnitude of the vector.

Two vectors are equal if they have equal magnitude and are in the same direction.

For vector additions, we study the triangle law and parallelogram law of vector additions.

Homework:

Workbook P 31, #1, #2, #3, #4, #5, #12, #15.