1. Warm up 1. Find the magnitude of this vector 2. A vector has Initial point (0,2) and terminal point (9,15). Write this vector in component form. 3. Find the angle this vector makes with it’s horizontal. 4. Find the dot product of and

2. ESSENTIAL QUESTION What is a Unit Vector, and how do I graph a vector in component form?

3. Math IV Lesson 54 Vectors Standard: MCC9‐12.N.VM.1(+)Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, | v|,||v||,v).

4.  Example: Graph vector

5. Multiples of Vectors Given a real number c, we can multiply a vector by c by multiplying its magnitude by c: v 2v2v -2v Notice that multiplying a vector by a negative real number reverses the direction.

6.  Find and graph the following 3u -3u 1/4u

7. Addition To add vectors, simply add their components. For example, if v = and w =, then v + w =. Other combinations are possible. For example: 4v – 2w =.

8. Magnitude The magnitude of the vector is the length of the segment, it is written ||v||. v (2,2) (5,6)

9. Unit Vectors A unit vector is a vector with magnitude 1. Example is a unit vector. Given a vector v, we can form a unit vector by multiplying the vector by 1/||v||. For example, find the unit vector in the direction :

10. Unit Vectors Notation A vector such as can be written as 3 + 4. For this reason, these vectors are given special names: i = and j =. A vector in component form v = can be written ai + bj.

11. WRITE THIS VECTOR USING UNIT VECTOR NOTATION

12. Heroic Quest 1.Graph this vector 2.Make a unit vector in the same direction as. 3.Write in unit vector form 4.Given u = and u = Find the dot product of the two vectors