PPT-Vectors in the Plane Section 11-A

Vectors When an object moves along a straight line its velocity can be determined by a single number that represents both magnitude and direction forward if positive and backward if negative. 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 Math 185 Vectors d) neither, because it is a direction only (Careful! You might think that the 15 Physics. K. Allison. Engagement. If a plane and the wind are blowing in the . opposite . direction, then the plane’s velocity . will . de. crease. .. Today we will learn how we can represent events like this.. SECTION VIEWS. OBJECTIVES. Understand sections and cutting-plane lines.. 2. Apply correct section-lining practices.. 3. Recognize and draw section lining for 10 different materials.. 4. Draw a section view given a two-view drawing.. Dr Chris Doran. ARM Research. 2. . Geometric Algebra in 3 Dimensions. Three dimensions. Introduce a third vector.. These all . anticommute. .. L2 S. 2. Bivector. products. The product of a vector and a . . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . Section 12.1. Three-Dimensional Coordinate Systems. Section 12.2. Vectors. Section 12.3. The Dot Product. Section 12.4. The Cross Product. Section 12.5. Lines and Planes in Space. Section 12.6. Cylinders and . Vector Spaces. MATH . 264 Linear . Algebra. Introduction. There are two types of physical quantities:. Scalars = quantities that can be described by numerical value alone (Ex: temperature, length, speed). Objectives:. To describe vectors. To solve problems that involve vector addition. Vector. : .  . Any quantity with magnitude (size) and direction. . Magnitude. : . The . distance. from the initial point to the terminal point.. The line and arrow used in Ch.3 showing magnitude and direction is known as the . Graphical Representation. Used when drawing vector diagrams. When using printed materials, it is known as . Algebraic Representation. Coordinates of an event in 4-space are (. ct,x,y,z. ).. Radius vector in 4-space = 4-radius vector.. Square of the “length” (interval) does not change under any rotations of 4 space. . How would you define a vector in 3D space?. 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.. Note-Taking Guide. I suggest only writing down things in . red. Review of Postulates from Chapter 1. Postulate 1 = Rule Postulate. Basically you can measure length/distance with a . ruler. Postulate 2 = Segment Addition Postulate.