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Transcript: where θ is the measure of the angle between a and b. Geometrically, this means that a and b are drawn with a common start point and then the length of a is multiplied with the length of the component of b that points in the same direction as a. The dot product can also be defined as the sum of the products of the components of each vector as: by: jackson THANK YOU Dot produce Magnitude or Length The dot produce is defined as follow for algebraic vectors in R2 and R3 Unit Vector Scalar projection and Vector projection The length of vector Formula Vector The length or magnitude or norm of the vector a is denoted by ‖a‖ or, less commonly, |a|, which is not to be confused with the absolute value (a scalar "norm"). The length of the vector a can be computed with the Euclidean norm: componentes If vector a =(a1,a2) and vector b=(b1,b2), then a.b= a1b1+a2b2 What is vector? This quantity is also called the component of b in the a direction (hence the notation comp). And, the vector projection is merely the unit vector a/|a| times the scalar projection of b onto a: Vector (English: vector, also known as vector) is a mathematical, physical and engineering science and other natural science in the basic concept, that has a size and direction (such as: East, South, West, North) geometric objects , Often known as an arrow symbol to distinguish it from other quantities. The dot product of two vectors a and b (sometimes called the inner product, or, since its result is a scalar, the scalar product) is denoted by a ∙ b and is defined as: Distance between two points Thus, mathematically, the scalar projection of b onto a is |b|cos(theta) (where theta is the angle between a and b) which from (*) is given by THANK YOU FOR WARTH If vector a=(a1,a2,a3) and vector b=(b1,b2,b3), then a.b=a1b1+a2b2+a3b3


Transcript: - The first uses of vector graphic displays was the US SAGE air defense system -1999: Vector graphics systems were retired from US air traffic control - Likely still in use in military an specialized systems - Vector graphics were also use on the TX-2 at the MIT (Massachusetts Institute of Technology) Lincoln laboratory by computer graphics pioneer Ivan Sutherland to run his program sketchpad in 1963 Vector graphics -geographic data in the pixel values as well as the pixel locations. -72 to 130 pixels per inch (PPI), -2400 dots per inch (DPI) THANK YOU! - Digital art is an artistic work or practice that uses digital technology as an essential part of the creative or presentation process VECTOR VS RASTOR Vector graphics -The World Wide Web Consortum (W3C) -Scrable Vector Graphics (SVG) -Scrable Vector Graphics Tinny (SVGT) -Bitmaps/ pixel arrays - Use of polygons to represent images in computer graphics -Based on vectors ( control point or nodes) -Definite position on the X- and Y- axes -Including such values as stroke color, shape, curve, thinckness and fill RASTOR - Engineering drawings are typically printed as bitmaps after VECTOR to RASTER conversion -"Vector graphics" is mainly used today in the context of 2D computer graphics -Raster display -Text / multimedia / 3D rendering - All modern 3D rendering is done using extension of 2D VECTOR graphics techniques Vector graphics RASTOR GRAPHICS -a way to painting a image line by line -Most modern computers have bit mapped displays Three dimensions GRAPHICS ART -Painter, Photoshop, Paint.NET, MS Paint, and GIMP, revolve around editing pixels, - unlike vector-based image editors, such as Xfig, CorelDRAW, Adobe Illustrator, or Inkscape, RASTOR GRAPHICS Vector graphics RASTOR GRAPHICS RASTOR GRAPHICS VECTOR RASTOR GRAPHICS -GIF, JPEG, and PNG, which are popular on the World Wide Web. -employed in video games and are also used in medical imaging such as MRI scanners. -The size of representation does not depend on the dimensions of the object - Rastor can't be vector Vector graphics Vector graphics

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