Pre-calc w-up 10/31.

Slides:

Advertisements

Similar presentations

Euclidean m-Space & Linear Equations Euclidean m-space.

Advertisements

Vectors in Three Dimensions

Objective: 8-4 Perpendicular Vectors1 Homework Answers 36. 5, 3i + 4j i – 34j Page i + 4j - k 16., i + 5j – 11k 18.,38.

Perpendicular Vectors Section 8-4. WHAT YOU WILL LEARN: 1.How to find the inner product and cross product of two vectors. 2.How to determine whether two.

Vectors. We will start with a basic review of vectors.

Vectors: planes. The plane Normal equation of the plane.

24. Dot Product of Vectors. What you’ll learn about  How to find the Dot Product  How to find the Angle Between Vectors  Projecting One Vector onto.

12.9 Parallel & Perpendicular Vectors in Two Dimensions

APPLICATIONS OF TRIGONOMETRY

Multiplication with Vectors

The Cross Product of Two Vectors In Space Section

Assigned work: pg.407 #1-13 Recall dot product produces a scalar from two vectors. Today we examine a Cross Product (or Vector Product) which produces.

Assigned work: pg. 449 #1abc, 2abc, 5, 7-9,12,15 Write out what “you think” the vector, parametric a symmetric equations of a line in R 3 would be.

10.5 Lines and Planes in Space Parametric Equations for a line in space Linear equation for plane in space Sketching planes given equations Finding distance.

Cross Product of Two Vectors

MCV4U The Cross Product Of Two Vectors The cross product also called a "vector product" only exists in R 3. a CROSS b, produces a vector quantity.

Section 13.4 The Cross Product. Torque Torque is a measure of how much a force acting on an object causes that object to rotate –The object rotates around.

Assigned work: pg. 468 #3-8,9c,10,11,13-15 Any vector perpendicular to a plane is a “normal ” to the plane. It can be found by the Cross product of any.

2.2 Day 2 Reflections and Rotations combined with Scaling The concept of transformations inspired art by M.C. Escher.

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.

Lesson 4.1- The Coordinate Plane, pg. 192

Chapter 2 Section 2.4 Lines and Planes in Space. x y z.

Assigned work: pg. 443 #2,3ac,5,6-9,10ae,11,12 Recall: We have used a direction vector that was parallel to the line to find an equation. Now we will use.

Copyright  1999 by James H. Money. All rights reserved. Except as permitted under United States Copyright Act of 1976, no part of this publication may.

Chapter 7 Review. Communication What does it mean to find the vector project of a onto b? Explain with an example. What does it mean to find the cross.

DOT PRODUCT CROSS PRODUCT APPLICATIONS

LAST CHAPTER!!!!!!! Yay!!!!!!!!! 8.1 & 8.2 Direct, Inverse & Joint Variation.

Warm Up. Equations of Tangent Lines September 10 th, 2015.

MOMENT ABOUT AN AXIS Today’s Objectives: Students will be able to determine the moment of a force about an axis using a) scalar analysis, and b) vector.

Wed. Apr. 15– Calculus Lecture #23.2 Vectors, Dot Products, Projections, and Planes ) If v and w are unit vectors, what is the geometrical meaning.

Composite 3D Transformations. Example of Composite 3D Transformations Try to transform the line segments P 1 P 2 and P 1 P 3 from their start position.

Today in Precalculus Turn in graded wkst and page 511: 1-8 Notes:

Section 3.3 Dot Product; Projections. THE DOT PRODUCT If u and v are vectors in 2- or 3-space and θ is the angle between u and v, then the dot product.

Warm up:. Problem: What is the angle between the vectors (1,2) and (-1, 3)?

1.1) RECTANGULAR COORDINATES Pg 9 # 1- Do Now!. Coordinate Plane  Label: x, y-axis, origin, quadrants  Plot points.

CSE 681 Brief Review: Vectors. CSE 681 Vectors Basics Normalizing a vector => unit vector Dot product Cross product Reflection vector Parametric form.

Objectives: Graph vectors in 3 dimensions Use cross products and dot products to find perpendicular vectors.

11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j.

12.10 Vectors in Space. Vectors in three dimensions can be considered from both a geometric and an algebraic approach. Most of the characteristics are.

Dr. Shildneck. Dot Product Again, there are two types of Vector Multiplication. The inner product,called the Dot Product, and the outer product called.

X axis y axis Points on a coordinate plane are written like this: (-8, 9) Move the dot.

Dot Product of Vectors Today’s Objective: I can calculate the dot product and projections of vectors.

CSE 681 Brief Review: Vectors. CSE 681 Vectors Direction in space Normalizing a vector => unit vector Dot product Cross product Parametric form of a line.

Normal Vector. The vector Normal Vector Definition is a normal vector to the plane, that is to say, perpendicular to the plane. If P(x0, y0, z0) is a.

Dot Product of Vectors.

Warm up 1.) (3, 2, -4), (-1, 0, -7) Find the vector in standard position and find the magnitude of the vector.

The Vector Cross Product

Dot Product and Angle Between Two Vectors

Section 3.4 Cross Product.

Elementary Linear Algebra

1-5 Writing Equations of Parallel and Perpendicular Lines

Vectors and the Geometry of Space

Lesson 12 – 10 Vectors in Space

Planes in Space.

5.2 The Factor Theorem & Intermediate Value Theorem

VECTORS APPLICATIONS NHAA/IMK/UNIMAP.

3.1 Graphing in 2-D Coordinates (Day 1)

Lines and Planes in Space

6.2 Dot Products of Vectors

By the end of Week 2: You would learn how to plot equations in 2 variables in 3-space and how to describe and manipulate with vectors. These are just.

We live in a Three Dimensional World

Chapter 9 Review.

Notes 7-2 The Coordinate Plane.

Math The Slope of a Line.

Angle between two vectors

10 Angular Momentum The Vector Nature of Rotation

Dots and Cross Products of Vectors in Space

Algebra 1 Notes Lesson 4-5: Graphing Linear Equations

Slope or Rates of Change

Presentation transcript:

Pre-calc w-up 10/31

8.4 Perpendicular Vectors If the inner product is _______ then the vectors are ___________ Often called the “dot product” and you say “a dot b” zero perpendicular

Ex1: find the inner product and determine if any are perpendicular. c)

Inner product of vector in space is extension of vector in a plane. Example 2

Cross product of two vectors in space is a vector Does not lie in the plane of the given vectors but is perpendicular. Cross product is written

To find the cross product, we need to review how to find the determinants of matrices - easy

Plug into formula Find the determinant Write it as an ordered triple – this is your cross product. How would I tell if it is perpendicular?

Find the inner product of new vector and v and new vector and w Summary: Homework: 8.4 pg 509 # 11-19, 21-26