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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

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 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…

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…

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

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

displacement

distance

velocity

speed

vector quantity describing a change in position

scalar quantity describing the path an object travels

vector quantity describing the displacement of an object over…

scalar quantity describing the distance of an object over time

displacement

vector quantity describing a change in position

distance

scalar quantity describing the path an object travels

scalar

magnitude and... direction

length

resultant

A quantity that has magnitude only is a

A vector always consists of _____ and _____.

The magnitude of a vector is indicated by the ___ of its arrow.

When vectors are added or subtracted, the net force is called…

scalar

A quantity that has magnitude only is a

magnitude and... direction

A vector always consists of _____ and _____.

scalar

vector

vector addition

vector subtraction

any positive or negative quantity that can be completely spec…

any quantity that requires a magnitude and direction for comp…

use parallelogram law of addition

scalar

any positive or negative quantity that can be completely spec…

vector

any quantity that requires a magnitude and direction for comp…

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

→... AB

magnitude

Scalars

Vectors

This represents a vector running from A to B, with its tail a…

The absolute value of the quantity.

A quantity with only the magnitude.

A quantity that requires magnitude and direction.

→... AB

This represents a vector running from A to B, with its tail a…

magnitude

The absolute value of the quantity.

vector

Scalar

resultant

Graphical Addition of vectors

A quantity with magnitude ( size) and direction.... examples: ve…

A quantity with magnitude only... examples: distance, speed, mas…

the arrow that extends from the tail of the first vector to t…

Using the ruler, draw all the vectors to the scale and connec…

vector

A quantity with magnitude ( size) and direction.... examples: ve…

Scalar

A quantity with magnitude only... examples: distance, speed, mas…

Vector

Component Form

Magnitude

Direction

An ordered pair of real numbers, denoted in component form as…

A vector expressed as an ordered pair ... <Change in x, change…

The length of the vector

The direction in which the arrow representing the vector is p…

Vector

An ordered pair of real numbers, denoted in component form as…

Component Form

A vector expressed as an ordered pair ... <Change in x, change…

Artboard

Object

Lines

Anchor Point

the area of the illustration that contains the printable part…

any shape, image, or text that can be moved, scaled, or edited.

an open ended path with two anchor points, which included str…

basic component of paths, which appear at the start and end o…

Artboard

the area of the illustration that contains the printable part…

Object

any shape, image, or text that can be moved, scaled, or edited.

What is a scalar?

What is a vector?

List of Scalars

List of Vectors

A quantity with magnitude (size) only.

A quantity with magnitude (size) and direction.

Mass, Distance, Temperature, Speed

Velocity, Weight, Acceleration, Displacement

What is a scalar?

A quantity with magnitude (size) only.

What is a vector?

A quantity with magnitude (size) and direction.

vector

scalar

notation of vector

magnitude of a vector

displacement in the plane and in three dimensions... has:... - ampl…

quantity that has a size but no direction... e.g. speed

- lower underlined case letter

length

vector

displacement in the plane and in three dimensions... has:... - ampl…

scalar

quantity that has a size but no direction... e.g. speed

Scalar

Vector

The components of a vector

Adding vectors

Number with units/ magnitude

Quantity with magnitude and direction

You can resolve a vector into a perpendicular components usin…

1. Find the components of each vector to be added... 2. Add the…

Scalar

Number with units/ magnitude

Vector

Quantity with magnitude and direction

Vector

speed

Scalar

Position Vector

quantity characterized by magnitude and direction

the rate of change of position with respect to time

A constant value, a quantity that only has magnitude

A vector that starts from origin in space

Vector

quantity characterized by magnitude and direction

speed

the rate of change of position with respect to time

scalar

vector

vector addition

vector subtraction

any positive or negative quantity that can be completely spec…

any quantity that requires a magnitude and direction for comp…

use parallelogram law of addition

scalar

any positive or negative quantity that can be completely spec…

vector

any quantity that requires a magnitude and direction for comp…

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

Non linear motion

How many directions does non-linear mo…

Can you use signs to find direction?

Vector

motion in a plane, 2 dimensional motion

infinite, but 4 main ones.

no

symbol used to represent a vector PQ

Non linear motion

motion in a plane, 2 dimensional motion

How many directions does non-linear mo…

infinite, but 4 main ones.

Vector

--->... AB

Opposite vectors

Equal vectors

Mathematical quantity having both magnitude and direction.

Represents a vectors running from A to B, with its tail at A…

Vector

Mathematical quantity having both magnitude and direction.

--->... AB

Represents a vectors running from A to B, with its tail at A…

Vector

Scalar

Displacement

Distance

A physical quanity with magnitude and direction

A pyiscal quanity with magnitude only

The change in position of an ojcet from a point of refernce

The total path length travelled by an object

Vector

A physical quanity with magnitude and direction

Scalar

A pyiscal quanity with magnitude only

Mass

Speed

Energy

Volume

The weight of an object, measured in the amount of atoms it h…

How fast an object is moving or how fast something is being d…

The ability to do work. Objects can have energy by virtue of…

The amount of space occupied by a 3D object, or region of spa…

Mass

The weight of an object, measured in the amount of atoms it h…

Speed

How fast an object is moving or how fast something is being d…

magnitude

Scalar

Vector

velocity

the relative size of an object

a quantity defined only by its magnitude

a quantity (such as velocity) that has size and direction

The ____ of an object is the rate of change of its position w…

magnitude

the relative size of an object

Scalar

a quantity defined only by its magnitude

What does a coordinate system provide?

Scalar

Scalars quantities involving time (3)

Scalar quantities involving motion (2)

A common frame of reference in which the quantities describin…

A scalar is a quantity that only has a numerical value (its M…

Time - t • Period - T • Frequency - f

Distance - d • Speed - v

What does a coordinate system provide?

A common frame of reference in which the quantities describin…

Scalar

A scalar is a quantity that only has a numerical value (its M…

what are 5 types of cloning vectors

what is the common vector host

what are the 3 characteristics of a pl…

what are the structural characteristic…

1) Plasmid... 2) Phage lambda like SV-40... 3) cosmid... 4) Phage M13…

- usually different strains of bacterial host, such as E.coli…

they have:... 1) ORI, origin of replication... 2) Drug resistance g…

1) circular... 2) double stranded DNA... 3) can be of various size…

what are 5 types of cloning vectors

1) Plasmid... 2) Phage lambda like SV-40... 3) cosmid... 4) Phage M13…

what is the common vector host

- usually different strains of bacterial host, such as E.coli…

Scalar

Vector

Resultant Vector

Projectile

Quantity having magnitude, but no direction

Quantity having both magnitude and direction

Sum of two or more vectors added together

Any object thrown forward

Scalar

Quantity having magnitude, but no direction

Vector

Quantity having both magnitude and direction

What is a vector?

True or false: You know a vector symbo…

True or false: You have two vectors, A…

If a y component of a vector is below…

Direction and magnitude.

False. It must be boldfaced.

False. Ax, Ay, Bx, and By are all of the scalar components.

Since components are scalar, then adding the y components are…

What is a vector?

Direction and magnitude.

True or false: You know a vector symbo…

False. It must be boldfaced.

What is a vector?

True or false: You know a vector symbo…

True or false: You have two vectors, A…

If a y component of a vector is below…

Direction and magnitude.

False. It must be boldfaced.

False. Ax, Ay, Bx, and By are all of the scalar components.

Since components are scalar, then adding the y components are…

What is a vector?

Direction and magnitude.

True or false: You know a vector symbo…

False. It must be boldfaced.

What is a vector?

What are some examples of vectors?

How do you calculate speed?

What does a distance-time graph look l…

It has a direction and a size.

Displacement... Velocity... Force... Acceleration

speed (m/s) = distance (m)/ time (s)

What is a vector?

It has a direction and a size.

What are some examples of vectors?

Displacement... Velocity... Force... Acceleration