8.3a-Vectors 33 22 11 Terms Operations Practice Problems.

8.3a-Vectors

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1Terms

Operations

Practice Problems

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What are Vectors Used For?

Vectors represent Paths of travel

i.e. distances Velocity

Direction and speed of an object Forces

WeightPressure

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Terms

Vector Directed line segment

Similar to a line or ray Has direction

Can be designated by: Ordered pairs Radians Degrees Graphically

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Terms (Cont.)

Vector (Cont.) Has Magnitude

How long the vector is Basically, the hypotenuse of a triangle if it is

not purely vertical or horizontal

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Notation

Ordered Pair Form Same as ordered pairs except <> is used

instead of ()

1,2

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Notation (Cont.)

Vector Name When possible use named points

Starting point is listed 1st

Ending point is listed 2nd

Arrow is placed over the lettersEx.

If no named points are available, “u” and “v” are typical

AB

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Notation (Cont.)

Vector Example

P

Q

PQ

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Notation (Cont.)

Magnitude Amount of force, weight, velocity, etc. Represented by:

Vector NameEnclosed by double vertical lines

PQ

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Addition/Subtraction of Vectors Combines the elements of 2 or more

vectors Result is called a Resultant Vector

7,24,3

74,23

3,5

1,51,5

11),5(5

0,10

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Graphic Representation of Vector Addition/Subtraction

Align vectors end-to-end without changing the angle

Draw a new vector from the beginning of the first vector to the end of the last vector

Name the resultant vector according to beginning and ending points

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Graphic Example of Addition of Vectors

AB

BC

ACBCAB

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Scalar Multiples

Changes the magnitude But not the angle Steps

Multiply each component of the vector by the scalar (number)

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Scalar Multiples Examples

4,32

)4(2),3(2

8,6

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Finding the Magnitude

Steps Square each element of the vector Add Take the square root Basically the Pythagorean Theorem

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Finding the Magnitude (Cont.)Find the Magnitude of

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i & j Coordinate System

In plain English…i is the x-axis, and j is the y-axis

ji 252,5

ji 434,3

jji 6606,0

iji 110110,11

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i and j Coordinate Example

Treat i and j as if they were variables

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Practice Problems

Page 601Problems 1-10, 29-36