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Topic: Vectors

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	Vectors
		The reason for this introduction to vectors is that many concepts in science, for example, displacement, velocity, force, acceleration, have a size or magnitude, but also they have associated with them the idea of a direction.
		Graphically, a vector is represented by an arrow, defining the direction, and the length of the arrow defines the vector's magnitude.
		The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line from the initial point of A to the final point of B, as illustrated in Panel 4.
	www.physics.uoguelph.ca /tutorials/vectors/vectors.html (1708 words)

	PlanetMath: vector
		Indeed, it is customary to depict a physical vector as an arrow.
		Essentially, given a finite dimensional abstract vector space, a choice of a coordinate frame (which is really the same thing as a basis) sets up a linear bijection between the abstract vectors and list vectors, and makes it possible to represent the one in terms of the other.
		Vectors are an essential scientific concept, indispensable for both the physicist and the mathematicians.
	planetmath.org /encyclopedia/Vector2.html (1189 words)

	Vector (spatial) - Wikipedia, the free encyclopedia
		A spatial vector is a special case of a tensor and is also analogous to a four-vector in relativity (and is sometimes therefore called a three-vector in reference to the three spatial dimensions, although this term also has another meaning for p-vectors of differential geometry).
		Vectors can be contrasted with scalar quantities such as distance, speed, energy, time, temperature, charge, power, work, and mass, which have magnitude, but no direction (they are invariant under coordinate rotations).
		The length or magnitude or norm of the vector a is denoted by
	en.wikipedia.org /wiki/Vector_(spatial) (3168 words)

	Vectors and Direction
		Vector diagrams were introduced and used in earlier units to depict the forces acting upon an object; such diagrams are known as free-body diagrams.
		The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow.
		The magnitude of a vector is represented by the length of the arrow; a scale is indicated (such as, 1 cm = 5 miles) and the arrow is drawn the proper length according to the chosen scale.
	www.glenbrook.k12.il.us /gbssci/phys/Class/vectors/u3l1a.html (1105 words)

	Animation Math in Lingo - A Tutorial & Demos: Vectors
		A vector can be used to specify a direction and a size (which is its length), so it is a useful term in describing these with one word.
		A vector is specified by its endpoint, [x,y].
		In 3 dimensions, a vector is specified by [x,y,z].
	www.jmckell.com /vectors.html (600 words)

	SparkNotes: SAT Physics: Vector Components
		For instance, the vector (3,4) is the vector whose tail is at the origin and whose tip is at the point (3,4) on the coordinate plane.
		Two vectors of particular note are (1,0), the vector of magnitude 1 that points along the x-axis, and (0,1), the vector of magnitude 1 that points along the y-axis.
		Vector decomposition is particularly useful when you’re called upon to add two vectors that are neither parallel nor perpendicular.
	www.sparknotes.com /testprep/books/sat2/physics/chapter4section5.rhtml (649 words)

	E-Example 7.1.1: Learning About Properties of Vectors and Vector Sums
		Adjust the vector by dragging either endpoint, or move it by dragging the dot on the vector.
		Vectors are used in numerous applications and are very important in the sciences and engineering.
		Vectors can be represented graphically, in the form of an arrow, or numerically, as length and angle measurements.
	standards.nctm.org /document/eexamples/chap7/7.1/index.htm (658 words)

	Vector Addition
		These rules for summing vectors were applied to free-body diagrams in order to determine the net force (i.e., the vector sum of all the individual forces).
		When the two vectors which are to be added do not make right angles to one another, or when there are more than two vectors to add together, we will employ a method known as the head-to-tail vector addition method.
		Once all vectors have been added head-to-tail, the resultant is drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish.
	www.glenbrook.k12.il.us /gbssci/phys/Class/vectors/u3l1b.html (1638 words)

	Classics in the History of Psychology -- Thurstone (1934)
		If a particle moves, we designate the movement by an arrow-head, a vector, in the direction of motion, but if it suits our convenience we put two arrowheads or more so that the observed motion may be expressed in terms that we have already been thinking about, such as the x, y, and z axes.
		In fact, the length of a test vector in the common factor space is the square root of its reliability.
		It is not inconceivable that the constellation of perceptual relations of Spearman will lie close to this central vector, because we may expect those tests to lie close to it which correlate best with judgments of intelligence, and that is the practical criterion by which intelligence tests have been constructed.
	psychclassics.yorku.ca /Thurstone (8879 words)

	ATCC: Vector Diagrams
		Expression vector for rapid purification of fusion proteins and release of proteins with fewer extraneous N-terminal amino acids.
		This vector is useful for gene knockout experiments in hosts with a non-revertable met15 auxotrophic marker gene mutation.
		This vector is useful for gene knockout experiments in hosts with a non-revertable ade2 auxotrophic marker gene mutation.
	www.atcc.org /Products/vectors.cfm (5361 words)

	VECTORS (Site not responding. Last check: )
		The length of the arrow representing a vector is definned to be the length, or magnitude, of the vector.
		The length of each vector corresponds to the magnitude of the force, and the direction to the direction of application of the force.
		The resultant vector is just the diagonal (having initial point in common with the two forces) of the parallelogram generated by the two forces.
	distance-ed.math.tamu.edu /Math640/chapter2/node2.html (750 words)

	Vectors
		The position point of a vector is defined using Cartesian co-ordinates: it uses the coordinates of the OX, OY and OZ axes where O is the origin.
		Let B be a typical point on the line with positive vector r and where d is a point on the line and n is a vector parallel to the line.
		Recall that the vector equation of a plane is (r - a).
	www.maths.surrey.ac.uk /interactivemaths/emmaspages/option2.html (940 words)

	Vectors (Site not responding. Last check: )
		Most of the elementary facts about vectors are the same in all dimensions (greater than 1), so you should have no trouble reading the three-dimensional discussion in the textbook for today.
		From a physical or geometrical point of view, "a vector is an arrow" with a certain length and a certain direction, and that concept is more fundamental than the representation of the vector by a string of 2 or 3 numbers.
		Notice that the new coordinate vector is obtained by vector subtraction of the coordinate vector of O' from the old coordinate vector of the point.
	www.math.tamu.edu /~fulling/coalweb/vectors.htm (1011 words)

	Vectors, A Vector Field Plotting Utility
		A common problem with using discrete vector arrows to represent a vector field is that as the size of the dataset increases, the vectors become too crowded and the rendering ceases to be intelligible.
		The length of each vector arrow is determined in relation to a vector reference magnitude that may be specified by the parameter VRM and a vector reference length that may be specified, as a fraction of the viewport width, by the parameter VRL.
		Vectors belonging to the dataset whose magnitude is equal to the reference magnitude are drawn at the reference length.
	ngwww.ucar.edu /ngdoc/ng4.3/supplements/vectors (18529 words)

	Vector Arithmetic
		The sum then is a vector from the tail of the first vector to the head of the last.
		I have already defined the scalar components of a vector as the coordinates of the head of the vector when its tail is at the origin.
		Remember that the sum of two vectors is a vector from the tail of the first to the head of the second.
	www.mcasco.com /p1va.html (1972 words)

	Vectors
		Suppose a vector isn't sitting with its tail at the origin?
		A history of the vector concept (which goes well beyond what we've touched on here) can be found in the
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /~klotz/Vectors/vectors.html (333 words)

	Vectors
		The unit vectors i, j, and k are chosen so that through the addition of multiples of themselves with each other, the three of them can describe all vectors possible in the space.
		This property of these three vectors (the dot product with themselves produces 1 and the dot product with each other produces 0) is what defines them as being a set of orthogonal, normalized vectors or orthonormal, for short.
		As the two vectors are rotated in towards each other, the resultant vector shortens until it disappears when the two overlap.
	www.cobalt.chem.ucalgary.ca /ziegler/educmat/chm386/RUDIMENT/MATHBAS/vectors.htm (1042 words)

	Tutorials - C++ Notes: Vectors
		After a vector has been declared specifying a certain number of elements, we can refer to individual elements in the vector using square brackets to provide a subscript or an index.
		Vectors have one important advantage with respect to arrays in C, C++ and in other languages: vectors can be resized during the execution of the program to accommodate extra elements as needed.
		A sequence is specified by a pair of iterators that indicate the beginning of the sequence and the end (given by an iterator to one-past-the-last element of the sequence).
	www.mochima.com /tutorials/vectors.html (1661 words)

	SparkNotes: Angles: Vectors
		A vector is essentially a line segment in a specific position, with both length and direction, designated by an arrow on its end.
		Vectors can be added and subtracted to one another, and multiplied and divided by scalars (number with magnitude but no direction).
		When two vectors are added or subtracted, the x-component of one vector is added or subtracted to the x-component of the other, and the same is done with the y-components of the vectors.
	www.sparknotes.com /math/trigonometry/angles/section4.rhtml (517 words)

	VECTORS (Site not responding. Last check: )
		Show students how to graphically add vectors "head to tail", by putting the head of the second vector to the head of the first vector and so forth until all vectors for that problem have been added.
		The main concepts revealed here were the addition of parallel vectors (positive or negative) depending on their direction, then adding two vectors at 90 degrees was shown.
		The vectors at various angles were shown to be quite simplified by using this method.
	www.iit.edu /~smile/ph8619.html (628 words)

	Basic Vector Operations
		Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.
		After finding the components for the vectors A and B, these components may be just simply added to find the components of the resultant vector R. The components fully specify the resultant of the vector addition, but it is often desirable to put the resultant in polar form.
		Vectors are resolved into components by use of the triangle trig relationships.
	hyperphysics.phy-astr.gsu.edu /hbase/vect.html (484 words)

	Maths - Vectors - Martin Baker
		Vectors are strongly related to matrices, they can be considered as a one directional matrix, or conversely, we could construct a matrix from a vector (drawn as a column) whose elements are themselves vectors (drawn as a row) :
		Regardless of whether we consider vectors as a special case of matrices, or matrices as vectors of vectors, or if we consider vectors and matrices as different types, using vectors and matrices together is very important.
		There are mathematical objects known a multivectors, these can be used to do many of the jobs that vectors do, but they don't have some of the limitations (for example vector cross product is limited to 3 dimensions and does not have an inverse).
	www.euclideanspace.com /maths/algebra/vectors (1816 words)

	vectors
		All other vectors in a coordinate system are expressed in terms of these vectors.
		Vectors are usually written with boldface type, and I shal adhere to that standard.
		The new vector has a magnitude which is equal to the area of the parallelogram.
	www.phys.psu.edu /~rutledge/vectors.html (773 words)

	Vector Calculator (Site not responding. Last check: )
		As you click and/or drag, the components, magnitude and direction for the vector are displayed (the direction is given in degrees, positive for vectors in the first and second quadrant and negative for vectors in the third and fourth quadrant).
		Once you have two vectors, clicking on the button labeled "Add" will display the vector sum (in magenta, or pink), and its components, magnitude and direction.
		Two auxiliary vectors are drawn in cyan (light blue) to help visualize the parallelogram; you can think of them as representing the original vectors, translated so as to perform the sum in a "tip-to-tail" fashion.
	comp.uark.edu /~jgeabana/java/VectorCalc.html (326 words)

	vectors
		The vector from (2,5) to (6,-2) is the same as the one from the origin to (4,-7)
		The sum (resultant) is the vector from the tail of the first to the head of the last vector.
		The vector velocity of the particle is v.
	quarknet.fnal.gov /toolkits/ati/vectors.html (502 words)

	Universal Cloning Vectors - Lentiviral Expression, Mammalian - Invitrogen
		Cloning vectors are small DNA vehicles designed to transport a foreign DNA fragment.
		Generate an expression clone by performing a recombination reaction between the entry clone and a Gateway® destination vector of choice.
		Several Invitrogen prokaryotic, yeast, insect and mammalian expressions vectors are adapted for one-step TOPO® Cloning of PCR products in both directional as well as non-directional formats.
	www.invitrogen.com /cloning_vectors.htm (965 words)

	Vectors (Site not responding. Last check: )
		An understanding of vectors is essential for an understanding of physics.
		A vector is a quantity that has two aspects.
		The white vector, positioned as a shadow on the y-axis, is the y-component of the yellow vector.
	id.mind.net /~zona/mstm/physics/mechanics/vectors/vectors.html (89 words)

	Vectors
		Suppose the given single vector is represented by the arrow AB in the drawing, and we wish to resolve it into the sum of two vectors directed along AA' and AA".
		Of those vectors, 10 are lined up with the x-direction, and vectors in the same direction (like head- and tail-wind velocities in the earlier example of the airplane) add up like ordinary numbers.
		The vector addition triangle of this example is at the bottom of the first figure of this section.
	www.phy6.org /stargaze/Svector.htm (1262 words)

	Technorati Tag: vectors (Site not responding. Last check: )
		Vectors maps the multiple contours of daily life in an unevenly digital era, crystallizing around themes that highlight the social, political, and...
		This vector is a school assignment, which was...
		Vector at CDW Shop CDW.com for the latest desktops, notebooks, printers, electronics and more.
	www.technorati.com /tag/vectors (509 words)

	Vectors in a plane
		Vectors AB and CD are equal if and only if there is a translation t such that t(A)=B and t(C)=D. The vector OO corresponds with the identical translation and is called the zero vector.
		The opposite vector of vector AB is vector BA corresponding with the inverse translation.
		A unity vector is defined by a vector with magnitude = 1.
	www.ping.be /~ping1339/vectors.htm (956 words)

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