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Topic: Vector sum

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	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)

	The Physics Classroom
		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).
		In this unit, the task of summing vectors will be extended to more complicated cases in which the vectors are directed in directions other vertical and horizontal directions.
		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.physicsclassroom.com /Class/vectors/u3l1b.html (1696 words)

	Vector Addition Tutorial
		vector (which represents the vector sum) is drawn from the tail of the first vector to the head of the last vector (see right side of the diagram below).
		In this example, using a ruler and protractor, we are able to get a resultant vector of about magnitude 11 and an angle of 102°.
		We have calculated the resultatnt vector's magnitude and direction but there is just one more thing to determine.
	www.1728.com /vectutor.htm (350 words)

	Vector sum (Site not responding. Last check: )
		Such a 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 threespatial dimensions, although this term also has another meaning for p-vectors ofdifferential 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
	www.therfcc.org /vector-sum-132058.html (1772 words)

	Phase calculation circuitry in digital television receiver - Patent 4710892
		It is well known that the instantaneous phase of the vector sum of a pair of orthogonal signals may be ascertained by generating the arctangent of the ratio of the instantaneous magnitude values of the respective signal components --i.e.,.theta.=Arctangent (Q/I).
		The output of the summing circuit 120 is fed via a bus 122 to an antilogarithm determining element 124, which may be a ROM (read-only-memory) that is programmed to produce on its output bus 126 values equal to the antilogarithms of the input values applied to the ROM as the respective address codes.
		The output of the summing circuit 134 on the bus 136 is applied to an antilogarithm determining element 138, which may also be a ROM, to produce on its output bus 140 a value corresponding to the expression II in the equation 10.
	www.freepatentsonline.com /4710892.html (4390 words)

	The Physics Classroom
		If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram.
		Add two or more velocity vectors and the result is a resultant velocity; add two or more force vectors and the result is a resultant force; add two or more momentum vectors and the result is...
		In all such cases, the resultant vector (whether a displacement vector, force vector, velocity vector, etc.) is the result of adding the individual vectors.
	www.physicsclassroom.com /Class/vectors/U3L1c.html (288 words)

	Addition of Forces
		During that discussion, the head to tail method of vector addition was introduced as a useful method of adding vectors which are not at right angles to each other.
		Once all vectors are added, the resultant (i.e., the vector sum) can be determined by drawing a vector from the tail of the first vector to the head of the last vector.
		The task of determining the vector sum of all the forces for the polar bear problem involves constructing an accurately drawn scaled vector diagram in which all five forces are added head-to-tail.
	www.glenbrook.k12.il.us /gbssci/phys/Class/vectors/u3l3a.html (1590 words)

	VECTOR MOMENTUM ANALYSIS
		VECTORS: A clear understanding of the concept of vectors and their components is mandatory to an understanding of accident reconstruction in general, and linear momentum in particular.
		The vector addition law states that if the arrows representing a set of vectors are laid tail to head in any order, the vector sum (the resultant vector) is represented by the arrow that connects the tail of the first to the head of the last.
		Vector sum analysis may be used as a graphical check on the mathematical results obtained from both vector momentum analysis and linear momentum.
	www.rec-tec.com /vector.html (2987 words)

	..:Physics 30 - {Unit I - Vector & Scalar Quantities - LessonI_2_1}:..
		Vectors are used to represent vector quantities on a diagram.
		Vectors can be added algebraically if the directions are the same or if you can make them the same with the addition of a minus sign.
		Vectors can also be added graphically on a neat, accurate and properly scaled diagram using the tail to tip method of addition.
	physics30.edcentre.ca /kindyn/lessoni_2_1.html (662 words)

	Vectors - Head to Tail Rule (Site not responding. Last check: )
		If two vectors having the same direction but different magnitude, their vector sum is the sum of the magnitudes in the same direction.
		If two vectors have the same magnitude and are in opposite directions their vector sum is a zero vector.
		If two vectors are in opposite direction and have different magnitudes, then their vector sum is the difference in magnitudes of the vectors in the direction of the vector with the larger magnitude.
	library.thinkquest.org /10030/4headta.htm (107 words)

	Power Supply Output Filter Design - Overshoot
		The magnitude of the overshoot is the vector sum of two orthogonal voltages, the output voltage before the load is removed and the current through the inductor times the characteristic impedance of the output filter, Zo = (L/C)^1/2.
		This is the orthogonal vector sum of the output voltage and the load current times the characteristic impedance and is illustrated in Figure 1.
		The ripple voltage across the capacitor (neglecting parasitic inductance) is a vector sum of voltage components across the capacitor's resistance and capacitance.
	www.smpstech.com /over0000.htm (1175 words)

	On the Cumulative Results of Quantum Measurements
		Thus, the "exhibited spin vectors" point in opposite directions parallel to the measurement angle, and their vector sum is zero.
		In any case, it's interesting that the "net spin vector" resulting from (the initial) measurements of the two spin-1/2 particles discussed above is different depending on whether you assume the pair correlations predicted by QM or those predicted by a typical "realistic" model.
		We'll now show that the average magnitude of this vector (versus the angle q) is in fact slightly smaller if we assume the correlation function predicted by quantum mechanics than if we assume the linear correlation predicted by a simple realistic model.
	www.mathpages.com /home/kmath419.htm (1568 words)

	Two-Dimensional Vector Sum - Physics programs - Brian's Casio Calculator Corner
		Enter the X-coordinate of the vector in response to the “x?” prompt and the Y-coordinate of the vector in response to the “y?” prompt.
		Enter the vector length in response to the “r?” prompt, and the vector angle in response to the “theta?” prompt.
		After the sum of the vectors has been displayed in rectangular coordinates, it is displayed in polar coordinates with the label “r,theta=”, followed by the distance (r) value of the vector, followed by the angle (theta) value of the vector in the chosen angular units.
	www.brianhetrick.com /casio/gpvecsum.html (1733 words)

	E-Example 7.1.2: Learning About Properties of Vectors and Vector Sums (Site not responding. Last check: )
		Students can see how changes in one of the summands affect the sum; for example, as the angle of the red vector is increased, the angle of the sum vector also increases.
		However, the relationship between the summands and the sum is not easily seen unless the summands have the same angle measure (in which case the lengths are added) or inverse measures (in which case the lengths are subtracted).
		Arrange the vectors head to tail by placing a velocity vector and the sum vector so they share a common initial point and then place the other velocity vector so its initial point is at the terminal point of the other velocity vector.
	standards.nctm.org /document/eexamples/chap7/7.1/part2.htm (861 words)

	Re: During Launch does 3 g's mean an acceleration of 19.6m/s^2 or 29.4m/s^2?
		As such, it's equal to the sum of all non-gravitational forces on the spacecraft, divided by the force gravity would exert on the spacecraft if it were sitting on the ground.
		The sum of non-gravitational forces divided by the spacecraft's weight on the ground is (35 million N / 18.6 million N) = 1.8 g.
		The vector sum of these forces is 4.3 million N at an angle of 19 degrees from the horizontal.
	www.madsci.org /posts/archives/may2001/988810519.Ph.r.html (864 words)

	Unify mass-energy-momentum (Site not responding. Last check: )
		Total momentum of a particle is the vector sum of all momentums in all spaces, hyper and normal.
		The rest mass of a particle is the vector sum of all hyperspace momentums divided by c, a constant.
		The kinetic energy of a particle is the vector sum of all normal space momentums multiplied by c, a constant.
	home.att.net /~bob.rutkiewicz/Unifymem.htm (125 words)

	Equilibrium (Site not responding. Last check: )
		The vector sum of all of the forces acting on a body is a single force called the net force.
		The vector sum of all the torques is a single torque called the net torque.
		When the aircraft is in equilibrium, the vector sum of these three forces is equal to zero.
	wright.nasa.gov /airplane/equilib.html (512 words)

	Momentum Analysis, Vector Sum Analysis, Diagrams
		A vector diagram is a way to draw a visual representation of the dynamics of the collision.
		Vector diagramming is a way that allows you to visually represent the collision and easily explain it to jury.
		In addition, the vector diagram will help you determine what the delta-V (change in velocity) and the principal direction of force (PDOF) are.
	www.collisionrecon.com /services/momentum-analysis.html (645 words)

	Vector-Summed Control
		It vectorially sums the induced voltage waveforms of motor windings and uses their zero-crossings to produce correctly-phased six-step commutation.
		This results in a vector which crosses zero at the phase-step transitions and can be used to commutate the motor.
		While either terminal is open, the induced-voltage vector sum of the phase-windings connected to it results in an induced-voltage waveform with the PWM drive waveform superimposed upon it.
	www.innovatia.com /Vector-Summed_Control.htm (408 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".
		The vector sum is now the diagonal of the rectangular box of which the three sums are the sides.
		The vector addition triangle of this example is at the bottom of the first figure of this section.
	www.phy6.org /stargaze/Svector.htm (1182 words)

	SearchEngine.net - Vector Addition
		Vector quantities are not fully described unless both magnitude and direction...
		The sum then is a vector from the tail of the first vector to the head of the last.
		If the concepts of graphical vector addition and subtraction are too abstract for you, here is an applet that should help:...
	www.searchengine.net /Vector_Addition.htm (215 words)

	AnatomyIntroduction (Site not responding. Last check: )
		For example, if the QRS vectors in leads I, II and III all have a positive polarity the range of intersection is +30 degrees to +90 degrees (shown in fl).
		On the other hand, if the QRS vector in lead I is positive and in leads II and III is negative, the range of intersection is -30 degrees to -90 degrees (shown in fl).
		If the QRS vector in lead I and II is negative and in lead III is positive, the range of intersection is -150 degrees to +150 degrees (shown in fl).
	www.technion.ac.il /~eilamp/leadoverlap1.html (477 words)

	Vector Sum Home
		Vector Sum Recordings is dedicated to producing high-caliber musical communications in a broad range of styles.
		Yet we also value the multiple-song format, as it provides a sonic narrative which is largely impossible within the framework of a single song.
		Trajectory Sketches by Vector Sum artist modulex is currently available at CDBaby.com.
	www.vector-sum.com (123 words)

	Rotating Calipers: vector sums of convex polygons (Site not responding. Last check: )
		The vector sums of polygons, also referred to as the Minkowski sum is used in motion planning.
		The vertices of P+Q are sums of co-podal pairs between P and Q.
		The algorithm's correctness follows from the main result; it has linear time complexity, from the fact that at each step one vertex for the vector sum is output, and since there are at most m+n of these, the total running time is m+n.
	cgm.cs.mcgill.ca /~orm/vecsum.html (349 words)

	Visualization of Parallel Impedances in the Z-Plane (Site not responding. Last check: )
		Find the vector, Z (subscript, L), which begins at the origin and terminates on the green line such that it intersects the green line at a right angle.
		The slope of the line for the Z vector is the negative inverse of the slope for the green line, because they are perpendicular to each other.
		The parallel combinations are shown as vector sums in the admittance-plane, or Y-Plane, which is the complex inverse of the Z-plane.
	www.mines.edu /~pbradfor/pimpedance.html (446 words)

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