PPT-4-1 Properties of Vectors

The line and arrow used in Ch3 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. 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 Other mathematical objects share these properties and we will investigate these functions polynomials 64257nite vector spaces matrices Because they have very similar structures techniques useful for dealing with one of these may be useful for others Topics 1 Vectors in I.Properties of II.Dot product, Norm and Distance properties in III.Pythagorean theorem in 2 Vector spaces I.Definition & Examples II.Vector Subspaces of III.Linear Indepen 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.. 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?. . 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 . 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). 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.. properties, addition, components of vectors . When you see a vector, think components!. Multiplication of vectors will come in later chapters.. Vectors have . magnitude. and . direction. .. Chapter 3: Vectors. 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..