PPT-8.6.2 – Orthogonal Vectors

At the end of yesterday we addressed the case of using the dot product to determine the angles between vectors Similar to equations from algebra we can talk about relationship of vectors as well Parallel. 1 Motivation A3 A2 Vectors A3 A21 Notational Conventions A4 A22 Visualization A5 A23 Special Vectors A5 A3 Vector Operations A5 A31 Transposition A6 A32 Equality A6 A33 Addition and Subtraction Orthogonal matrices. independent basis, orthogonal basis, orthonormal vectors, normalization. Put orthonormal vectors into a matrix. Generally rectangular matrix – matrix with orhonormal columns. Square matrix with orthonormal colums – . Five-Minute Check (over Lesson 8-4). Then/Now. New Vocabulary. Key Concept: Dot Product and Orthogonal Vectors in Space. Example 1: Find the Dot Product to Determine Orthogonal Vectors in Space. Example 2: Angle Between Two Vectors in Space. define . scalar and vector quantities and . give . examples.. (. b) draw and use a vector triangle to . determine the resultant of two vectors such as displacement, velocity and force.. (c) Use trigonometry to determine the resultant of two vectors.. Which of the following is the odd one out?. Mass. Speed. Force. Temperature. Distance. Elephant. Which of the following is the odd one out?. Mass. Speed. Force. Temperature. Distance. Elephant. Scalars. Objectives. :. Distinguish between vector and scalar quantities. Add vectors graphically. Scalar. – a quantity that can be completely described by a number (called its magnitude) and a unit.. Ex: length, temperature, and volume. In the case of vectors, we have a special vector known as the . unit vector. Unit Vector. = any vector with a length 1; direction irrelevant . Two special unit vectors we look at the most;. i. = {1, 0}. Is a . number. with units. It can be positive or negative.. Example: distance, mass, speed, Temperature…. Chapter 3: . VECTORS. 3-2 . Vectors and Scalars. Scalar. Is a quantity with both . direction. GENETIC. . ENGINEERING. Genetic engineering is the manipulation of genetic materials which can be introduced in the host organisms and thus change the phenotype of the host organism.. A.D. . Rollett. Vectors, Matrices, . Rotations. , . Axis Transformations. Most of the material in these slides originated in lecture notes by Prof. Brent Adams (. now emeritus . at BYU). . Last revised: 9 Nov. ‘11. Hung-yi Lee. Outline. Reference: Chapter 7.1. Norm & Distance. Norm. : Norm of vector v is the length of v. Denoted . Distance. : The distance between two vectors u and v is defined by .  .  .  . In some cases, we will have to decompose a vector into a sum of two separate vectors. Recall; most vectors may be written as some variation of the special unit vectors {1,0} and {0,1}. With vectors, sometimes they may not be pointing or oriented in the proper direction. Any vector can be resized by multiplying it by a real number (scalar).. Multiplying by positive scalar changes magnitude only.. Multiplying by a negative scalar changes the magnitude and its direction.. The characteristic roots of the (. p×p. ) matrix . A. are the solutions of the following determinant equation: . Laplace expansion. is used to write the characteristic polynomial as. :. Since (.