PPT-Section 9 – 4 Vectors

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. 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 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.. A . scalar. quantity . can be described by a . single number. , . with some meaningful . unit. 4 oranges. 20 miles. 5 miles/hour. 10 Joules of energy. 9 Volts . Vectors and scalars. A . scalar. quantity . Motivating Question. : An Airplane flies north with an airspeed of 575 mph. If the wind is blowing 30° north of east at 50 mph, what is the speed of the plane as measured from the ground? What if the wind blew south of west?. . 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.. 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 . Scalar. A . SCALAR. is ANY quantity in physics that has . MAGNITUDE. , but NOT a direction associated with it.. Magnitude. – A numerical value with units.. Scalar Example. Magnitude. Speed. 20 m/s. 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). 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.. Read Chapter 1.6-1.9. Scalars and Vectors. All measurements are considered to be quantities. In physics, there are 2 types of quantities – . SCALARS. . AND . VECTORS. .. Scalar. quantities have only magnitude.. A vector is a DNA molecule that has the abil­ity to replicate autonomously in an appropri­ate host cell and into which the gene of inter­est (a foreign genetic sequence) is integrated. When we insert a foreign genetic sequence into the vector the aim is either to obtain numer­ous copies of the gene of interest or to obtain the product of that.. or phages are viruses that specifically infect bacteria. . Viral vectors are those in which gene of interest is incorporated in the genome of virus.. The phage particle attaches to the outer surface of bacterium and injects its DNA into the cell..