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vector

magnitude

scalar

Pythagorean Theorem

A measurement with magnitude and direction.... Represented with…

the amount of a measurement

A measurement that just has amount or magnitude... example: mass…

method used to recombine component sums or vectors that are p…

vector

A measurement with magnitude and direction.... Represented with…

magnitude

the amount of a measurement

Distance between P₁ and P₂

What is distance between P₁(2,1,5) and…

Standard Equation of a Sphere: radius-…

Find center and radius of sphere, x² +…

|P₁P₂|=√((x₂-x₁)²+(y₂-y₁)²+(z₂-z₁)²)

√45

(x-x₀)²+(y-y₀)²+(z-z₀)²=a²

center: (-3/2,0,2), radius √(21)/2

Distance between P₁ and P₂

|P₁P₂|=√((x₂-x₁)²+(y₂-y₁)²+(z₂-z₁)²)

What is distance between P₁(2,1,5) and…

√45

Vector quantities

Vector

Resultant of two vectors

Resolving a vector

Have both magnitude and direction, such as Displacement, Velo…

represented by an arrow whose length represents the magnitude…

Adding the vectors tail-head-tail-head; vector diagram drawn…

Replacing the vector with two components that add to form the…

Vector quantities

Have both magnitude and direction, such as Displacement, Velo…

Vector

represented by an arrow whose length represents the magnitude…

|P₁P₂|=√((x₂-x₁)²+(y₂-y₁)²+(z₂-z₁)²)

√30

(x-x₀)²+(y-y₀)²+(z-z₀)²=a²

(2,-3,1)

Distance between P₁ and P₂

What is the distance between P(3,1,5) and R(-2,3,6)

Standard Equation of a Sphere with radius-(a) and center- (x₀…

Find the center of sphere, x² +y² +z² +4x -6z +2 = 0

|P₁P₂|=√((x₂-x₁)²+(y₂-y₁)²+(z₂-z₁)²)

Distance between P₁ and P₂

√30

What is the distance between P(3,1,5) and R(-2,3,6)

Vector quantities

Vector

Resultant of two vectors

Resolving a vector

Have both magnitude and direction, such as Displacement, Velo…

represented by an arrow whose length represents the magnitude…

Adding the vectors tail-head-tail-head; vector diagram drawn…

Replacing the vector with two components that add to form the…

Vector quantities

Have both magnitude and direction, such as Displacement, Velo…

Vector

represented by an arrow whose length represents the magnitude…

vector

magnitude

scalar

Pythagorean Theorem

A measurement with magnitude and direction.... Represented with…

the amount of a measurement

A measurement that just has amount or magnitude... example: mass…

method used to recombine component sums or vectors that are p…

vector

A measurement with magnitude and direction.... Represented with…

magnitude

the amount of a measurement

vector

magnitude

scalar

Pythagorean Theorem

A measurement with magnitude and direction.... Represented with…

the amount of a measurement

A measurement that just has amount or magnitude... example: mass…

method used to recombine component sums or vectors that are p…

vector

A measurement with magnitude and direction.... Represented with…

magnitude

the amount of a measurement

vector

Pythagorean theorem

hypotenuse

right triangles

A quantity that has both size and direction.

a²+b²=c²... a squared plus b squared = c squared, where c is the…

the longest side of a right triangle

Triangles containing one 90 degree angle

vector

A quantity that has both size and direction.

Pythagorean theorem

a²+b²=c²... a squared plus b squared = c squared, where c is the…

b) -2 N

a) 130km... b) 0

58.3 km

The polygon method

Given: F1 = 3 N due East and F2 = 5 N due West, what is the s…

A car travels 65 km due North, then 65 km due South.... a) What…

Given a displacement due North of 50 km and a displacement du…

The graphic method of adding vectors by placing the tail of t…

b) -2 N

Given: F1 = 3 N due East and F2 = 5 N due West, what is the s…

a) 130km... b) 0

A car travels 65 km due North, then 65 km due South.... a) What…

Vector

Scalar

Free-fall acceleration

Horizontal Velocity

A physical quantity that... has both magnitude and direction.

A physical quantity that... has only magnitude.

Acceleration due to gravity is called

This will always be constant

Vector

A physical quantity that... has both magnitude and direction.

Scalar

A physical quantity that... has only magnitude.

graphical representation

algebraic representation

resultant vector

Pythagorean relationship

An arrow or an arrow-tipped line segment is called a ___ of a…

an ___ of a vector is represented by an italicized letter in…

a vector that is the sum of two or more other vectors

This states that the sum of the squares of the two sides of a…

graphical representation

An arrow or an arrow-tipped line segment is called a ___ of a…

algebraic representation

an ___ of a vector is represented by an italicized letter in…

Arthropods comprise what proportion of…

Economic entomology deals with this ty…

Medical entomology deals with these 2…

Diplopoda is...

More than 3 quarters

Interspecific competition for a common resource

1) direct parasitism, injury, irritations, or annoyance and 2…

A class of the phyla arthropoda which includes millipedes.

Arthropods comprise what proportion of…

More than 3 quarters

Economic entomology deals with this ty…

Interspecific competition for a common resource

Resultant

Scalar Multiplication

Components

Normal Force

sum of vectors

multiplying a vector by a real number or by a quantity with u…

two perpendicular vectors that add to a given vector

A force exerted by one object on another in a direction perpe…

Resultant

sum of vectors

Scalar Multiplication

multiplying a vector by a real number or by a quantity with u…

Vector quantities

Vector

Resultant of two vectors

Resolving a vector

Have both magnitude and direction, such as Displacement, Velo…

represented by an arrow whose length represents the magnitude…

Adding the vectors tail-head-tail-head; vector diagram drawn…

Replacing the vector with two components that add to form the…

Vector quantities

Have both magnitude and direction, such as Displacement, Velo…

Vector

represented by an arrow whose length represents the magnitude…

component

projectile

resolution

resultant

part of a resultant vector, usually along the x or y axis

An object moving through space and affected only by gravity

finding components of a resultant vector

The net result of a combination of two or more vectors

component

part of a resultant vector, usually along the x or y axis

projectile

An object moving through space and affected only by gravity

Vector

Scalar

Vector Components

Hypotenuse

A quantity that has both magnitude and direction.

A quantity that has magnitude only.

X and Y coordinates that specify a vector in 2 dimensional sp…

The side in a right triangle that lies opposite from the righ…

Vector

A quantity that has both magnitude and direction.

Scalar

A quantity that has magnitude only.

vector

scalar

unit vector

equilibriant

a quantity with magnitude and direction... ex: force, accelerati…

a quantity with magnitude (size) only

a vector with a magnitude of 1 [unit] ... expresses direction us…

angle measure

vector

a quantity with magnitude and direction... ex: force, accelerati…

scalar

a quantity with magnitude (size) only

vector

magnitude

scalar

cosine function

A measurement with magnitude and direction.... Represented with…

the amount of a measurement

A measurement that just has amount or magnitude... example: mass…

Used in vector resolution to find the adjacent component of a…

vector

A measurement with magnitude and direction.... Represented with…

magnitude

the amount of a measurement

a.b

What does the scalar product do?

Is the scalar product commutative or a…

What does a negative scalar product me…

|a||b|cosθ

Projects one vector onto another and multiplies their magnitu…

Commutative

The vectors point in opposite directions

a.b

|a||b|cosθ

What does the scalar product do?

Projects one vector onto another and multiplies their magnitu…

vectors

vectors have

in order to draw vector, must have

conversion factor

quantifiable way to describe value and direction. arrows

magnitude and direction

key or conversion factor

represents how length is related to a forces strength. x cm =…

vectors

quantifiable way to describe value and direction. arrows

vectors have

magnitude and direction

vector

magnitude

scalar

Pythagorean Theorem

A measurement with magnitude and direction.... Represented with…

the amount of a measurement

A measurement that just has amount or magnitude... example: mass…

method used to recombine component sums or vectors that are p…

vector

A measurement with magnitude and direction.... Represented with…

magnitude

the amount of a measurement

Length or magnitude of a vector

Theorem used to calculate Length / mag…

How do we multiply two vectors

What is a unit vector

‖A‖ = √(Ax² + Ay² + Az²)

Pythagoras' Theorem

Dot Product - also called the scalar product

A Unit Vector has a magnitude of 1. Remember it has a MAGNITU…

Length or magnitude of a vector

‖A‖ = √(Ax² + Ay² + Az²)

Theorem used to calculate Length / mag…

Pythagoras' Theorem

magnitude

displacement

scalar

component form

the size or amount of a quantity, including units of measurem…

a vector quantity representing the change in the position of…

a quantity that can be described completely by its magnitude

the process of describing a vector in terms of two perpendicu…

magnitude

the size or amount of a quantity, including units of measurem…

displacement

a vector quantity representing the change in the position of…

vector

vector

added

direction

Force, like velocity and displacement, is a _____ quantity.

A ______ quantity can be represented by an arrow-tipped line…

Vectors can be _______ by placing the tail of one vector at t…

When adding two vectors, neither the length nor the of either…

vector

Force, like velocity and displacement, is a _____ quantity.

vector

A ______ quantity can be represented by an arrow-tipped line…

vector

scalar

commutative law for addition

tip-to-tail method

a quantity which contains magnitude and direction

a quantity which contains only magnitude

vectors can be added in any order

the arrow of one vector is connected the the end of another v…

vector

a quantity which contains magnitude and direction

scalar

a quantity which contains only magnitude

magnitude direction

equal

triangle law

Magnitude

A vector quantity has both ________ and ________.

If two vectors have the same magnitude and direction, they ar…

Two vectors are added using the '________ ________'.

What is the modulus, |a|, of a vector?

magnitude direction

A vector quantity has both ________ and ________.

equal

If two vectors have the same magnitude and direction, they ar…

Vector

Developing Competence

Managing Emotions

Moving through Autonomy toward Interde…

A comprehensive picture of the psychosocial development durin…

Physical, Intellectual, Interpersonal

Acting on feelings in appropriate ways; recognizing, acceptin…

Emotional and Instrumental Dependence; Recognizing the value…

Vector

A comprehensive picture of the psychosocial development durin…

Developing Competence

Physical, Intellectual, Interpersonal

Vector quantity

Scalar quantity

Arrow

Resultant displacement

A quantity that has direction and magnitude (i.e. Velocity)

A quantity that are specified only by a number and units; no…

The symbol for a vector

The sum of the vectors (V1 and V2)

Vector quantity

A quantity that has direction and magnitude (i.e. Velocity)

Scalar quantity

A quantity that are specified only by a number and units; no…

Vector

Resultant

Equilibrant

Tip to tail method

Quantity with both magnitude and direction

Single vector that represents the sum of 2 or more vectors

Vector equal in magnitude, but opposite in direction to the r…

Arrow tip of one vector is perpendicular to the tail of other…

Vector

Quantity with both magnitude and direction

Resultant

Single vector that represents the sum of 2 or more vectors

Finding the angle between two vectors

Finding magnitude of a vector

Component method

Magnitude and direction method

Get solution using component method and mag. and dir. method.…

Square each under a square root.

Multiply the two vectors

Multiply the magnitude of both vectors together.... Multiply tha…

Finding the angle between two vectors

Get solution using component method and mag. and dir. method.…

Finding magnitude of a vector

Square each under a square root.

#include <vector>

can grow and shrink

vector<int> v;

vector<int> v(N);

What must be at the top of the program to include vectors?

What is different about vectors than arrays?

How do we declare a vector name v with integer elements?

How do we declare a vector named v with N amount of integer e…

#include <vector>

What must be at the top of the program to include vectors?

can grow and shrink

What is different about vectors than arrays?