Vectors CPT
Jagbir Bhullar
MCV4U1-03

Vectors CPT
Jagbir Bhullar
MCV4U1-03

Distance Between 2 points

Distance Between 2 points

Midway between points

Midway between points

Collinear points

Collinear points

Vector Introduction

Points

Equal Vectors

Equal Vectors

Zero Vector

Zero Vector

Triangle law of addition

Triangle law of addition

The Vector

The Vector

Scalar Multiplication

Scalar Multiplication

Collinear Vectors

Collinear Vectors

Properties of Vector addition

Properties of Vector addition

Commutative property of addition

Commutative property of addition

Associative Property of Addition

Associative Property of Addition

Distributive Property of Addition

Distributive Property of Addition

Real Life Application

Architecture

Architecture

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Structural Engineers are types of architects which help in the design of large-scale structures such as bridges or skyscrapers. The role of these structural engineers is to make stable structures which can survive the elements. They calculate forces acting on buildings and the weight of the building to design a safe structure. Commonly a resultant force must be calculated from the composition of forces such as hurricanes, tornados and tsunamis. the forces as previous mentioned all contain magnitudes and directions supporting in the use of calculating vectors to prepare safe structures. 

Sports

Sports

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In many sports the application of vectors are used and valued. Vectors are used to determine where a baseball may land or the distance travelled by a football. Vectors provide an exact measurement for which a player needs to make that goal and score a point for their team. Using Force, direction and distance a basketball player is consistently able to control where their ball is thrown. In baseball a board is often kept to check the velocity of each pitch thrown, these values help for teams to separate players between the good and the bad. In mixed martial arts the force produced by a person is constantly tested and calculated to see hitting force and speed.

Medical Tools

Medical Tools

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In hospitals machines are commonly used to diagnose patients and to find the cause of injury. These machines such as the MRI, X-ray, ultrasound and CT-scan are used to locate the exact location of an injury. commonly in MRI's a magnetic field is used to locate these injuries, the only way this magnetic field works is by the use of magnetic field vectors. These vectors are used to control the strength and direction the magnetic resonance imaging are applying to someone getting diagnosed inside the MRI.

Dot Product

Dot Product

Cross Product

Cross Product

Intersection of 3 Planes

Lines and Planes

Rearranged

Rearranged

Commutative

Commutative

Distributive

Distributive

Magnitudes

Magnitudes

Associative

Associative

Projections

Scalar Projections

Scalar Projections

Vector Projections

Vector Projections

Calculations

Calculations

Find a,b,c

Find a,b,c

Distributive Law

Distributive Law

Scalar Law

Scalar Law

not commutative

not commutative

Skew Lines

Skew Lines

Coincident Lines

Coincident Lines

Parallel Lines

Parallel Lines

Equation of Lines in R2

Equation of Lines in R2

Slope and Direction Vectors

Equations in R3

Parametric

Parametric

Symmetric

Symmetric

Plane

Plane

Line

Line

cartesian equation

cartesian equation

parametrics

parametrics

Parametric

Parametric

intersecting lines at a point

intersecting lines at a point

Intersecting

Intersecting

Coincident

Coincident

Parallel

Parallel

Skew

Skew

2 Planes

Coincident

Coincident

Parallel

Parallel

Intersect at line

Intersect at line

Point to Line with cartesian coordinate

Point to Line with cartesian coordinate

Point to Line with vector equation

Point to Line with vector equation

Point to Plane

Point to Plane

Intersects π at a point

Intersects π at a point

Line Parallel to π

Line Parallel to π

Line is on π

Line is on π

2 planes intersecting at line

2 planes intersecting at line

2 parallel planes

2 parallel planes

2 coincident planes

2 coincident planes

3 planes intersect at 1 point

3 planes intersect at 1 point

3 planes are parallel

3 planes are parallel

2 planes are parallel 2 planes are 
parallel and distinct the third is
not parallel

2 planes are parallel 2 planes are
parallel and distinct the third is
not parallel

3 coplanar but not parallel

3 coplanar but not parallel

Line and plane

2 planes

3 planes

3 planes are coincident

3 planes are coincident

3 planes intersect in a line

3 planes intersect in a line