What is Resultant: Definition and 512 Discussions

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.
The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usual resultant) is a generalization, introduced by Macaulay, of the usual resultant. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).

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  1. N

    What is the magnitude of the resultant of the following vectors?

    Homework Statement What is the magnitude of the resultant of the following vectors? 5N, East 8N, 30 degrees West of North 2N, East 7.5N, 23.5 degrees West of South Is there a way to solve this using a calculator? Any help would be great.
  2. N

    Magnitude of the resultant

    Homework Statement Find the magnitude of the resultant of the following series of vectors. 120N, North 190N, 60 degrees East of North 70N, 10 degrees East of South 150N, 45 degrees South of West I have similar questions like these and not sure how to answer them, if anyone can help...
  3. D

    Finding Vector with Known Vector and Resultant Vector

    Homework Statement There are two forces. One has a magnitude of 8 N and acts at an angle of 30 degrees on the resultant vector. The resultant vector is 15 N. Homework Equations equations for components (|a|cosx for horizontal and |a|sinx for vertical) cos law and sin law basic trig...
  4. R

    Finding angle for this resultant vector

    Hello I am working on this problem and just can't figure it out... Consider two displacements, one of magnitude 3.0 m and another of magnitude 3.8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 5.7 m, (b) 2.5 m, and (c) 3.6 m...
  5. R

    Finding the resultant vector

    Homework Statement In the figure below shows the path taken by a drunk skunk over a level ground, from initial point i to final point f. The angles are θ1 = 30, θ2 = 50, and θ3= 80, and the distance are d1 = 5.00 m, d2 = 8.00 m, and d3 = 12.0 m. What are the (a) magnitude and (b) angle of the...
  6. B

    Magnitude and coordinate direction angles of the resultant force.

    Problem is here http://engineeringhomework.net/statics/FG02_32-03UNP62.JPG Determine the magnitude and coordinate direction angles of the resultant force. I don't know where to start on this one.
  7. O

    How do I make the resultant vector equal zero?

    Homework Statement Three forces are applied to an object, as indicated in the drawing. Force 1 has a magnitude of 33.0 Newtons (33.0 N) and is directed 30.0° to the left of the +y axis. Force 2 has a magnitude of 26.0 N and points along the +x axis. What must be the magnitude and direction...
  8. P

    Acceleration without resultant force (rotating body)

    Hello there. I have some difficulty in understanding the condition for a rigid body standing still (or rotating). If we have a body, let's say a yoyo which is somehow pierced through the center and attached in a way that it's center of mass can't move, but the yoyo can rotate if we apply...
  9. jegues

    Rotating the Resultant Force on a Charge

    Homework Statement See figure attached for problem statement and figures given Homework Equations The Attempt at a Solution See figure attached for my attempt. I'm obtaining x^2 = negative in the end so I'm guessing I must have done something wrong, I'm just not quite sure...
  10. K

    Resultant Force on Charge in the middle of square

    Homework Statement (a) Find the resultant force on a negative charge of -3q, placed at the center of a square of side b, which has charges on the 4 corners, respectively, q, 2q, -4q, 2q in clockwise order. (Magnitude and direction)Homework Equations F= k*q1*q*(1/ r^2) Ftotal= F15 + F25 + F35...
  11. J

    Resultant Force Help: Converting m/s to mph

    I was relearning some physics and I came across this problem. Kyle and Paul, two NHL players, are playing hockey against each other and Kyle checks Paul, on center ice. They hang on to each other so the collision is inelastic. Assume Kyle weighs 90kg and Paul weighs 80kg. Kyle was skating at...
  12. O

    Magnitude of resultant forces

    Homework Statement Forces with magnitude of 200 Newtons and 300 Newtons act on a hook. The angle between the two forces is 65°. Find the magnitude of the resultant of these forces. Round your answer to 2 decimal places. (Hint: write the 300 pound force as a vector in the direction of the...
  13. A

    Resultant vector of an isosceles triangle?

    Homework Statement what is the resultant vector of an isosceles triangle? Homework Equations R^2=a^2+b^2-4abcos(theta) The Attempt at a Solution The books answer R=2acos(theta/2) Using the formula above, and knowing that a=b in a isosceles triangle I am getting...
  14. B

    Calculating Resultant Force of a Noncurrent System

    Homework Statement Calculate the magnitude, direction and sense of the resultant force of the noncurrent force system shown, determine where the resultant intersects the bottom of the shape with respect to Point A Homework Equations...
  15. P

    Easy Resultant Velocity Problem

    I need help in this problem! It goes: For the winter, a duck flies 10.0m/s south against a gust of wind with a speed of 2.5m/s. What is the resultant velocity of the duck?
  16. A

    Is the torque of a couple equal to the resultant torque?

    Homework Statement If the only forces acting in a system are a couple, will the torque of the couple be the resultant torque of the sytem? Homework Equations The Attempt at a Solution
  17. A

    Resultant force on aircraft door

    Homework Statement The air pressure at the altitude an aircraft is flying at is 28kPa. If the pressure inside the cabin is maintained at 100kPa, what is the resultant force on a door of area 2m^2 in the side of the aircraft? Homework Equations The Attempt at a Solution I am not...
  18. T

    Calculating Resultant Velocity: A Guide for Long Distance Swimmers

    A long distance swimmers starts out swimming a steady 2mph at 30 degrees south of west. A 5mph current is flowing at 10 degrees north of east. What is the swimmers resultant velocity?
  19. C

    Compute Resultant Algebraically - Help

    Homework Statement Its an old exam question compute algebraicially the resultant of the following coplanar forces: 100 N at 30 degrees, 141.4N at 45 degrees and 100N at 240 degrees Homework Equations to be honest I have no idea what they are asking me in this question The Attempt...
  20. D

    How to find the angle between the resultant and the X axis?

    Homework Statement How do you find the angle between the resultant and the x-axis? Please refer to the link in the picture. I just don't know how to get theta which is 10.26 degrees. Homework Equations https://www.physicsforums.com/attachment.php?attachmentid=29314&d=1287763774 The...
  21. D

    What is the resultant of these vectors?

    Homework Statement What is the resultant of these vectors? (Pictures included). Homework Equations Their can either go Straight up vertically Straight right horizontally Southwest (shooting 45 degree) Northeast (shooting upwards 45 degrees) The Attempt at a Solution Thanks!
  22. G

    Direction of resultant displacement?

    Homework Statement http://i287.photobucket.com/albums/ll124… Homework Equations At the end of the walk, what is the magnitude of the person’s resultant displacement measured from the starting point? I found this answer to be 595.7697375 m after finding the vertical velocity to be...
  23. S

    Is position and resultant vectors are same?

    Hi all.. I am new at this forum... I have a question.. Please tell me about Position vector and Resultant vector? According to my point of view, both vectors are same.. And tell me about free vector and null vector.. Thanks in advance...
  24. F

    Finding Resultant Vector: A=220g@0°, B=100g@110°, C=160g@260° | Homework Help

    Homework Statement We are given three components: Component A has a magnitude of 220g at 0 degrees, Component B has a magnitude of 100g at 110 degrees, and Component C has a magnitude of 160g at 260 degrees. We are supposed to find the resultant vector. HELP! :) Homework Equations...
  25. H

    Find the resultant displacement from the cave entrance

    Homework Statement While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75 m north, 250 m east, 100 m at an angle 30° north of east, and 160 m south. Find the resultant displacement from the cave entrance. Homework Equations The...
  26. K

    Answer "Homework: P & Q Forces Resultant & Angle

    Homework Statement The resultant of two forces P & Q is √3Q. It make angle of 30o with the direction of force P. Show that P is either equal to Q or equal to 2Q. Homework Equations R2 = P2 + Q2 + 2PQcosΘ tanα = QsinΘ/[P+QcosΘ] The Attempt at a Solution From R2 = P2 + Q2 + 2PQcosΘ...
  27. K

    Discover the Magnitudes and Angle Between Two Forces: Resultant Forces Homework

    Homework Statement The sum of two forces is 24N. There resultant is act right angle to the smaller of the two forces which is 12N. Find the magnitudes of the two forces & the angle between them. Homework Equations R2 = P2 + Q2 + 2PQcosΘ tan α = QsinΘ/ (P+QcosΘ) The Attempt at a...
  28. V

    Calculating Resultant Force: Comparing Methods and Identifying Errors

    Ok so I have something like this...not drawn to scale http://i53.tinypic.com/303l5k6.gif I can see that with the law of cos I can get 49N However...with this other method where you set Sum of F=0 With sqrt(Fx^2+Fy^2)=R sqrt((40*cos(20)+20*cos(30))^2+(40*sin(20)-20*sin(30))^2) I...
  29. M

    What does the resultant velocity represent in a problem?

    Homework Statement When finding the resultant velocity in a problem what does the resultant stand for Homework Equations ((x2+y2)1/2 The Attempt at a Solution I understand I use the equation above to find the resultant velocity but is the resultant the same thing as displacement...
  30. P

    Determine Resultant Force-Couple on T6 Vertebra at F2

    Homework Statement A chiropractor applies a thrust to the spinous process of T6. The magnitude is 400 N and it is applied 90 degrees to the y-axis. While this occurs the superior disc applies a force to the T6 body of 615 N, 75 degrees to the x-axis. The inferior disc applies a force to...
  31. P

    Resultant Force Acting on T6 Vertebrae

    A chiropractor applies a thrust to the spinous process of T6. The magnitude is 400 N and it is applied 90 degrees to the y-axis. While this occurs the superior disc applies a force to the T6 body of 615 N, 75 degrees to the x-axis. The inferior disc applies a force to the T6 body of 620 N, 70...
  32. C

    Resultant Force Acting On Springs : Confused

    Homework Statement Suppose we have 2 insulated metal rods each measuring 40 cm. Now,the 2 metal rods are connected with 3 identical springs each of length 20 cm (force constant 2.0 N/m) in parallel. A current of 20A is passed through each metal rod in opposing directions. What is the extension...
  33. V

    Finding the resultant displacement vector.

    Homework Statement In order to get from her classroom too the lab without going through the crowded rotunda, Jodie walks 14m (E), 42m(S), 32m(W), 13m(S), and 9m(E). Draw a scale diagram to represent all the initial displacement vector and the resultant displacement vector in Jodie's walk to...
  34. L

    Calculating Resultant Force of Two Forces: 8N and 11N at 30 Degrees

    two forces with a magnitude 8N and 11N act on a large object. The angle between the forces is 30 degrees. Calculate the magnitude of the resultant force. the answer is 18.4 in the back of the book I drew a diagram and made a triangle... i was trying to use the triangle rule but like i...
  35. G

    Resultant direction of aircraft

    Homework Statement in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ? Homework...
  36. A

    How to find the resultant of 3d vector?

    i have a vector ai+bj+ck is the resultant equal to sqrt(a^2+b^2+c^2). if so how do i explain it mathematically? i know the resultant of a 2d vector is equal to sqrt(a^2+b^2) and it can be proved from pythagoras theorem? any ideas??
  37. G

    Resultant direction of aircraft

    in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?
  38. D

    Equilibrium. Vectors and resultant forces.

    Homework Statement An object is at equilibrium if all the forces on it add up to zero. There's a beam which weights 124N 40degrees above the horizontal that is supported in equilibrium by a 100-N pull 30degrees above the beam and a force F at the floor. The third force on the beam is the 124-N...
  39. A

    Resultant Force: 40N in Negative X Direction

    Resultant force? A particle is said to be in static equilibrium if the resultant of all forces is applied to it is zero. Find the force that must be applied to a particle that produces static equilibrium if there are two forces, each of 40N applied so that one acts 60o above the positive x-axis...
  40. E

    Resultant time dilation from both gravity and motion

    When a frame is moving in relation to an observer in his rest frame at infinity, and the frame is in a gravitational well, is the resultant time dilation simply the sum of the motional and gravitational dilation, e.g...
  41. P

    Determine the magnitude of the resultant force

    Homework Statement If F_{B} = 5kN and the resultant force acts along the positive u axis, determine the magnitude of the resultant force. The attempt at a solution F_{Rx} = F_{R}cos 30 F_{Ry} = F_{R}sin 30 F_{Rx} = 3 + 5cos\theta F_{Ry} = 5sin\theta Therefore, \frac{3 +...
  42. C

    Is the beam in equilibrium with three forces acting on it?

    A heavy beam is located on two supports, so that there are 3 forces acting on it. The beam is in an equilibrium. There are two forces on top pulling it up and one force pulling it down. The two forces are on each side and the one on its own on the bottom is in the middle pulling down. Am...
  43. C

    Calculate the magnitude and direction of the resultant force on the object.

    Hey, I have the following question. How do I work this out: There is an object 9N<-----------[OBJECT]--->3N--->4N...[The ---> represent the direction in which the object is being pulled, and the 3N and 4N pull into the same direction. Now its asking me: 1. Calculate the magnitude and direction...
  44. 0

    Calculating Resultant Force

    I'm I on the right track here? Homework Statement Determine the resultant force and acceleration for a box of mass 15kg being pushed with a force of 9N and a force of friction 6N acting to oppose.Homework Equations Force = Mass * Acceleration The Attempt at a Solution Force = 9N Resultant...
  45. 5

    How to Find the Resultant Vector of this Quadrilateral ?

    This question is from a "Solved Problems" book where they give the solutions but I'm not able to get the reason ! Question : ABCD is a quadrilateral.Force BA,BC,CD and DA act at a point.Their resultant is : Options: a. 2AB b. 2DA c. 2BC d. 2BA The given answer is : 2BA Formulas Related...
  46. M

    Different representations of SU3 and resultant multiplets

    I have a very basic query about multiplets. In the SU(3) approach strongly interacting particles, quarks and hadrons are the basis vectors of irreducible representations of SU(3). Now, quarks and hadrons are definite properties with define eigenvalues of hypercharge and isospin: to put it...
  47. M

    Finding the Resultant Amplitude & Phase: A Practice Problem

    Hi, this isn't homework but a practice problem. A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. The amplitudes are 0.25, 0.20, 0.15, and the face difference between the first and second is 450 and between the second and...
  48. L

    Statics - Balancing moment and resultant force

    Homework Statement Replace the force system with a resultant and specify where its line of action intersects AB from point B. so I guess the imagine didn't work... http://yfrog.com/htstaticspicp I realize it is very small I apologize for that, if anything in the picture is unclear please let...
  49. F

    Find the Moment (Torque) of the resultant in 3-D (Statics)

    Hey guys... This problem is driving me bonkers. I really am not asking you to calculate anything but I only ask how to figure out how to get r to use τ = r x F . My professor did not even teach us anything about resultants and 3-d moments :grumpy: Homework Statement Homework Equations...
  50. C

    Calculating resultant forces given FBD

    Homework Statement A truck of mass 8000 kg is accelerating at 5.0 m/s2 up a hill of inclination 4 degrees to the horizontal The friction forces on the truck add up to 5500 N. What force does the truck exert against the road in the direction of travel? What force does the road exert on...
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