Warm up

1. Find the magnitude of this vector<-3,15> 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. <3,7> 4. Find the dot product of <-7,12> and <0,-3>

ESSENTIAL QUESTION

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

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).

Example: Graph vector <3,9>

Multiples of Vectors

Given a real number c, we can multiply a vector by c by multiplying its magnitude by c:

v2v -2v

Notice that multiplying a vector by anegative real number reverses the direction.

Find and graph the following3u-3u1/4u

Addition

To add vectors, simply add their components.

For example, if v = <3,4> and w = <-2,5>, then v + w = <1,9>.

Other combinations are possible. For example: 4v – 2w = <16,6>.

Magnitude

The magnitude of the vector is the length of the segment, it is written ||v||.

v

(2,2)

(5,6)

Unit Vectors

A unit vector is a vector with magnitude 1.Example <3/5, 4/5> 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 <3,4>:

Unit Vectors Notation

A vector such as <3,4> can be written as

3<1,0> + 4<0,1>.

For this reason, these vectors are given special names: i = <1,0> and j = <0,1>.

A vector in component form v = <a,b> can be written ai + bj.

WRITE THIS VECTOR USING UNIT VECTOR NOTATION

<7,-12>

Heroic QuestHeroic Quest1. Graph this vector <3,-2> 2. Make a unit vector in the same direction as <3,-

2>. 3. Write <3,-2> in unit vector form4. Given u = <3,2> and u = <7,3> Find the dot

product of the two vectors