 A vector is a mathematical object that has both magnitude (size) and direction  Students will be able to use basic vector operations and the dot product

 Vector: has both magnitude and direction. Represented with an arrow  Magnitude: length of the arrow  A vector has an initial point and terminal point to determine direction  If segments have the same magnitude they can represent the same vector

 The initial point must be at the origin  Complete a transformation of both points to find the new terminal point in component form.  What are the component forms of the two vectors shown here?  (this makes it easier to determine the magnitude)

 Let u = and v =  What is |u + v|  What is |u - v|

 If the number is greater than 1, then only the magnitude changes  If the number is less than one, then the magnitude changes and the direction is reversed

 Given u = what is ◦-u◦-u ◦ 1/2u ◦3u◦3u

 Multiplying two vectors together  Expresses and angular relationship  v = and w =  Then the dot product is v 1 w 1 + v 2 w 2  If the dot product = 0, the two vectors are normal, or perpendicular to each other.

Are the following vectors normal?,

 Pg. 813  #7 – 12, 20 – 34 even  14 problems