# Study sets matching "vectors math"

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vector

Scalars

displacement

Column vector form

a quantity that has size (magnitude) and direction; i.e. displ…

Quantities determined by magnitude alone; i.e. distance and sp…

the difference between your initial position and your final po…

Use of horizontal and vertical component in a column to descri…

vector

a quantity that has size (magnitude) and direction; i.e. displ…

Scalars

Quantities determined by magnitude alone; i.e. distance and sp…

Position vector

What is a unit vector

How to find a unit vector

I, j

Starting from (0,0)

A vector in the same direction of a magnitude of 1

Divide the vector by the magnitude of the vector

I - unit along x axis. J- unit along y axis

Position vector

Starting from (0,0)

What is a unit vector

A vector in the same direction of a magnitude of 1

vector

Scalars

displacement

Column vector form

a quantity that has size (magnitude) and direction; i.e. displ…

Quantities determined by magnitude alone; i.e. distance and sp…

the difference between your initial position and your final po…

Use of horizontal and vertical component in a column to descri…

vector

a quantity that has size (magnitude) and direction; i.e. displ…

Scalars

Quantities determined by magnitude alone; i.e. distance and sp…

Component form of a vector

magnitude of a vector

Unit vector

Find the angle between two vectors (u a…

Combines the horizontal and vertical components of a vector in…

Square root of the component form squared and added together

(1/magnitude of vector) multiplied by the original vecot

Cos(angle)= (UxV/(magnitude of v) x (magnitude of U))

Component form of a vector

Combines the horizontal and vertical components of a vector in…

magnitude of a vector

Square root of the component form squared and added together

Scalar Quantities

Vectors

Displacement

Equal Vectors

have size but not direction (distance and speed)

allow quantities to be defined by size (magnitude) and directi…

the difference between initial position and final position

same direction, same magnitude but not necessarily in same pla…

Scalar Quantities

have size but not direction (distance and speed)

Vectors

allow quantities to be defined by size (magnitude) and directi…

Dot Product

Angles Between Vectors

dot product properties

Orthogonal

if u=<u1,u2> and v=<v1,v2> than u (dot) v=u1v1+u2v2

between 0 and 180 degrees, cos= u (dot) v/ (magnitude)u (magni…

u(dot)v=v(dot)u... u(dot)u=(magnitude)u(squared)... 0(dot)=0... u(dot)(…

the vectors u and v are if u(dot)v=0

Dot Product

if u=<u1,u2> and v=<v1,v2> than u (dot) v=u1v1+u2v2

Angles Between Vectors

between 0 and 180 degrees, cos= u (dot) v/ (magnitude)u (magni…

Resultant Vector

Component Vector

Magnitude

Direction

The vector sum or "result" of two or more component vectors... -…

Vectors that are being added together... - must be tip to tail*…

Value, represented by size of arrow, measured with ruler

The path that an object is moving or facing, represented by an…

Resultant Vector

The vector sum or "result" of two or more component vectors... -…

Component Vector

Vectors that are being added together... - must be tip to tail*…

When are A B and C collinear?

What are the two equations involving ar…

How do you write a line in vector, para…

how do you find angle between lines

vector AB=k(vector BC)

(magnitude of vector a)(magnitude of vector b)sinx=magnitude o…

vector: <x y z> = <point> + <direction>t... parametric: x=(x poin…

-find direction for each (in vector form or parametric)... -cosx…

When are A B and C collinear?

vector AB=k(vector BC)

What are the two equations involving ar…

(magnitude of vector a)(magnitude of vector b)sinx=magnitude o…

conjugate

modulus

real axis

imaginary axis

opposite of the imaginary part of a complex number

a complex's numbers length or distance from the origin

aka x-axis

aka y-axis

conjugate

opposite of the imaginary part of a complex number

modulus

a complex's numbers length or distance from the origin

Midpoint

Position Vector

Vectors

Magnitude

Key Point: The position vector of the midpoint of AB is 1/2 (a…

Key Point: AB is the position vector of point B minus the posi…

Key Point: If a//b, b=ta for some scalar t

size= magnitude= distance= length

Midpoint

Key Point: The position vector of the midpoint of AB is 1/2 (a…

Position Vector

Key Point: AB is the position vector of point B minus the posi…

Same Magnitude and Direction

Same Magnitude and Opposite Direction

xi + yj + zk = Given Vector, i, j, and…

Any vector with a magnitude = 1, also w…

Equal Vectors

Negative Vectors

Unit Vector Form

Unit Vectors

Same Magnitude and Direction

Equal Vectors

Same Magnitude and Opposite Direction

Negative Vectors

vector

Scalars

displacement

Column vector form

a quantity that has size (magnitude) and direction; i.e. displ…

Quantities determined by magnitude alone; i.e. distance and sp…

the difference between your initial position and your final po…

Use of horizontal and vertical component in a column to descri…

vector

a quantity that has size (magnitude) and direction; i.e. displ…

Scalars

Quantities determined by magnitude alone; i.e. distance and sp…

vector

standard unit vectors

unit vector in the direction of that ve…

adding vectors method 1

geometric quantity with direction and magnitude

magnitude of 1, i = <1,0> j = <0,1>

(1/|u|) * u

tip to tail method

vector

geometric quantity with direction and magnitude

standard unit vectors

magnitude of 1, i = <1,0> j = <0,1>

Pythagorean Theorem

Theta

Adjacent

Opposite

a² + b² = c²

θ -Greek letter used for angles, the angle θ is always between…

adj (next to) - the side on the other side of theta, together…

opp (across from) - the side across from the theta

Pythagorean Theorem

a² + b² = c²

Theta

θ -Greek letter used for angles, the angle θ is always between…

how to get <AB> from points A and B

Length of vector <AB>

direction of vector <AB> ("unitized")

Standard position of vector?

subtract coordinates, B-A => <x2-x1,y2-y1,z2-z1>

|<AB>| = sqrt(x^2+y^2+z^2)

dir(<AB>) = <AB>/|<AB>| = i.e. <AB>/sqrt(x^2+y^2+z^2)

coming from the origin

how to get <AB> from points A and B

subtract coordinates, B-A => <x2-x1,y2-y1,z2-z1>

Length of vector <AB>

|<AB>| = sqrt(x^2+y^2+z^2)