Intersections of Lines in 2 Space Three Cases: 1) 2) 3)

Slides:

Advertisements

Similar presentations

Vector Equations in Space Accelerated Math 3. Vector r is the position vector to a variable point P(x,y,z) on the line. Point P o =(5,11,13) is a fixed.

Advertisements

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

HW #17 pg. 194 #5-7, 15-17, 21, 26, 29.  Theorem 3.8  If two lines intersect to form two congruent angles that are a linear pair, then the lines must.

Basic Facts about Parallel Planes

IB HL Adrian Sparrow Vectors: the cross product.

6.3 Basic Facts About Parallel Planes Objective: recognize lines parallel to planes and skew lines Use properties relating parallel lines relating parallel.

T5.3 – Lines in Space IB Math SL1 - Santowski 5/20/20151IB Math SL1 - Santowski.

Parallel Lines and Planes By: B R C VERSION 2. Read the symbol || as is parallel to. Arrowheads are often used in figures to indicate parallel lines.

6.3 Parallel Plane Facts Objectives: 1.Recognize lines parallel to planes, parallel lines and skew lines 2.Use properties relating parallel planes and.

1.4/1.5 Points, Lines, Planes & Segments Warm-up (IN) Learning Objective: to describe and sketch relationships between points, lines, planes, rays and.

x y no x y yes.

 Find segment lengths using midpoints and segment bisectors  Use midpoint formula  Use distance formula.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

POP QUIZ Keystone Geometry. D F C O E G BA 1) Name the circle. 2) Name a radius. 3) Name the diameter. 4) Name a chord. 5) Name a tangent. 6) Name a secant.

9.1 INTERSECTION OF TWO LINES To find the intersection of two lines L(1) and L(2) :  Write both equations in parametric form. L(1)= (x1,y1,z1) + t(a,b,c)

Mathematics. Session Three Dimensional Geometry–1(Straight Line)

Specialist Maths Vectors and Geometry Week 4. Lines in Space Vector Equation Parametric Equations Cartesian Equation.

1.3 Lines and Planes. To determine a line L, we need a point P(x 1,y 1,z 1 ) on L and a direction vector for the line L. The parametric equations of a.

LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.

OBJ: to find the greatest common factor of two or more numbers.

Vector Space o Vector has a direction and a magnitude, not location o Vectors can be defined by their I, j, k components o Point (position vector) is a.

1. Given vectors a, b, and c: Graph: a – b + 2c and 3c – 2a + b 2. Prove that these following vectors a = 3i – 2j + k, b = i – 3j +5k, and c = 2i +j –

Spaghetti Geometry Place a piece of spaghetti on your paper and tape it down. We will let this represent a LINE A Line goes on __________________ (arrows.

1.5 Do Now: Look for a pattern in the table. Write an equation that represents the table. x0123 y x0123y ) 2.)

Understanding Points & Lines Essential Question: How do you use undefined terms as the basic elements of geometry?

Further vectors. Vector line equation in three dimensions.

8/29/2011. A C B 

Geometry Lesson 8 – 2 Extended Coordinates in Space Objective: Use ordered triple with distance and midpoint formulas.

XDI RDF Graphing V x+y $has +x+y $has +x+y +x/$has/+y +x+y +x+y $has +x+y/$has/+z +x/$has/+y+z +x+y+z +x+y+z $has +z +x+y+z $has 3 4 Full.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

Skew Lines. The two given lines given are skew (i.e. they do not meet). What is the shortest distance between them? shortest distance.

Graphing in 3-D Graphing in 3-D means that we need 3 coordinates to define a point (x,y,z) These are the coordinate planes, and they divide space into.

Unit 2: Properties of Exponents Jeopardy

8.2A Factoring using Distributive Property

Vectors in space Two vectors in space will either be parallel, intersecting or skew. Parallel lines Lines in space can be parallel with an angle between.

Simplifying Variable Expressions

Do Now 1. For A(–4, 8) and B(5, 8), find the midpoint of AB.

6.3 Solving Systems of Linear Equations in Three Variables

Algebra with Whole Numbers

Lesson 3.1 Lines and Angles

Intersection between - Lines, - Planes and - a plane & a Line

Lines and Planes in Space

Algebra 1 Mini-Lessons 20x2 + 5x

Simplifying Variable Expressions

Entry Task What are the first 3 steps for constructing a line through point P that is parallel to the line. Reflection Question: What are the main concepts.

Parametric Equations of lines

(x2,y2) (3,2) (x1,y1) (-4,-2).

المعايير الدولية لإعداد التقارير المالية للمنشآت الصغيرة ومتوسطة الحجم

Simplifying Variable Expressions

What is dimension?.

4.3 Subspaces of Vector Spaces

Unit 2: Properties of Exponents Jeopardy

Points, Lines, and Planes QUICK DRAW FOR POINTS!

Simplifying Variable Expressions

Who Wants to be an Equationaire?. Who Wants to be an Equationaire?

Simplifying Variable Expressions

Section Graphing Linear Equations in Three Variables

Space groups Start w/ 2s and 21s 222.

Vector Equations in Space

Simplifying Variable Expressions

Finding Shortest Distances

Solving systems of 3 equations in 3 variables

HW 13: red text p. 415 #s 1 – 12. y = x 2. y = -x slope = 1 slope = -1

Angles and Parallel Lines

Planes, segments and rays can also be perpendicular to one another if they intersect at 90 degree angles.

Parallel and Perpendicular Lines

3.1 Parallel Lines and Transversals

Presentation transcript:

Intersections of Lines in 2 Space Three Cases: 1) 2) 3)

Examples: 1) x – 2y = 5 x + 4y = 8 2) -15x + 18y = -8 5x – 6y = 3 3) 4x – 3y = 1 8x – 6y = 2

4) (x,y) = (-3,5) + s(4,-9) (x,y) = (2,-1) + t(-4,9)

5) (x,y) = (1,0) + s(-3,4) (x,y) = (-3,6) + t(5,2)

Intersection of Lines in Three Space 4 Cases: 1) 2) 3) 4)

Examples: 1) (x,y,z) = (4,2,-2) + s(-3,4,1) (x,y,z) = (0,3,1) + t(-3,4,1)

2) (x,y,z) = (7,2,-6) + s(2,1,-3) (x,y,z) = (3,9,13) + t(1,5,5)

3) (x,y,z) = (5,-4,-2) + s(1,2,3) (x,y,z) = (2,0,1) + t(2,-1,-1)

The Distance between 2 Skew Lines

Example: Find the distance between the two lines (x,y,z) = (5,-4,-2) + s(1,2,3) (x,y,z) = (2,0,1) + t(2,-1,1) HW p.156 #1,2,4,5,6, 9abcdf,12ab