/
VECTORS Scalar Multiplication – Resizing Vectors VECTORS Scalar Multiplication – Resizing Vectors

VECTORS Scalar Multiplication – Resizing Vectors - PowerPoint Presentation

stefany-barnette
stefany-barnette . @stefany-barnette
Follow
360 views
Uploaded On 2018-11-07

VECTORS Scalar Multiplication – Resizing Vectors - PPT Presentation

Any vector can be resized by multiplying it by a real number scalar Multiplying by positive scalar changes magnitude only Multiplying by a negative scalar changes the magnitude and its direction ID: 720250

vector vectors find magnitude vectors vector magnitude find adding unit scalar tails direction written join multiplying parallelogram heads form

Share:

Link:

Embed:

Download Presentation from below link

Download Presentation The PPT/PDF document "VECTORS Scalar Multiplication – Resizi..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

VECTORSSlide2

Scalar Multiplication – Resizing Vectors

Any vector can be resized by multiplying it by a real number (scalar).Multiplying by positive scalar changes magnitude only.Multiplying by a negative scalar changes the magnitude and its direction.Slide3

Resizing Written Vectors

Example: Given u = <3, 5>, find 4u.

“distribute”

4

u

=

4

<3, 5>

= <

4

x3,

4

x5>

= <12, 20>Slide4

Adding Vectors – Geometrically

“Parallelogram Method”Given two vectors, to add them geometrically, you can use a parallelogram.First, join the vectors initial points (tails).

Second, create two more vectors that are equal to the original vectors. Place them where the tails meet the heads of the first set and join their heads to make a parallelogram.Finally, the resultant vector of this addition is the diagonal from the joined tails to the joined heads.Slide5

Adding Vectors – Geometrically

“Parallelogram Method”

u

v

u

+ v

Join the tails of the two vectors you are adding.

Create two equal vectors.

Join the new vectors’ tails to the heads of the original.

Draw the diagonal from the TAIL to the HEAD.Slide6

Adding Vectors in Written Form

Adding vectors in written forms is fairly simple. Basically you just have to follow the order of operations.In component form:Multiply through by any scalars.

Add horizontal components, Add vertical componentsIn Linear combinations:Combine like terms.Slide7

Adding Vectors in Written Form

Examples. Given u = <3, 5> and v = <2, -4> find the following vectors.3

u + 2v =

2

u

-

v

=

3<3, 5> + 2 <2, -4>

= <9, 15> + <4, -8>

= <13, 7>

2<3, 5> - <2, -4> = <6, 10> + <-2, 4> = <4, 14>Slide8

Unit Vectors

A unit vector is a vector of magnitude 1 (in any direction).

To find a unit vector in a specific direction (the direction of another given vector), you must “divide” the given vector using scalar multiplication so that the new vector’s magnitude is 1. Find the magnitude of the given directional vector.

Multiply by the reciprocal of the magnitude.Slide9

Unit Vectors

Example: Find the unit vector in the same direction as <-3, 4>.

||<-3, 4

>||

=

 

=

 

=

 

=

 

1. Find the magnitude of <-3, 4>

2. Find the unit vector by multiplying by the reciprocal.

<-

3,

4>

 

=

<

,

>

 Slide10

Assignment

Assignment 2Alternate Text – On Blogp. 433-434 #13-22, 25-28, 35-40, 45-46