What is Position vector: Definition and 110 Discussions

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P.
In other words, it is the displacement or translation that maps the origin to P:





r

=



O
P

→




{\displaystyle \mathbf {r} ={\overrightarrow {OP}}}
The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.

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  1. karush

    MHB Find the position vector of P

    The vector equations of two lines are given below $r_1=\pmatrix {5 \\ 1}+2\pmatrix {3 \\ -2}$, $r_2=\pmatrix {-2 \\ 2}+t\pmatrix {4 \\ 1}$ The lines intersect at the point P. Find the position vector of P this being in form of r=a+tb where a is the the position vector and b is the...
  2. Philosophaie

    Formulating Position Vector with f(t)

    How do you formulate the Position Vector: x^m = [t____x____y____z] x^m = [f(t)____ax/2*t^2 + vx*t + x0____ay/2*t^2 + vy*t + y0____az/2*t^2 + vz*t + z0] dx^m / dt = [df(t) / dt____ax*t + vx____ay*t + vy____az*t + vz] What do you put in the"t" position "f(t)".
  3. S

    Griffiths Chapter 10 del cross position vector

    I am working through chapter 10 of Griffith’s electrodynamics (for fun and in my spare time). While I don’t have a formal bucket list, getting to an understanding of how Newton’s third law is not as straightforward for electrodynamics has been on my mental bucket list. I am an engineer not a...
  4. T

    How to find equation for a position vector function on a parabaloid?

    Homework Statement Velocity vector given by r'(t)=<cos(t), -sin(t), -2sin(t)> Surface that the position vector needs to lie on: z=x2+y2 Homework Equations Integral of r'(t) will give position function The Attempt at a Solution I know that the integral of r'(t) will give me...
  5. J

    Particle in plane, find position vector

    A particle of mass m moves in the x-y plane; its acceleration in m/s^2 is given by the expression ->a = −6iˆ for t ≥ 0 secs . At t = 0 secs, the object is at the point (x(sub 0), y(sub 0) = (36,0); coordinates are in meters. At t = 4 secs , the object is at the point x(sub 0), y(sub 0) = (36...
  6. C

    Position vector R of a particle moving x-y plane

    Hello, new to these forums! I'm working on my UPI homework, and I just want to verify if I'm doing something correctly. The problem: The position vector r of a particle moving in the x - y plane given by r = (2t^3)i + (6-7t^4)j, where r is in meters and t is in seconds. Calculate r v a...
  7. D

    MHB Angular Velocity for Constant Separation Distance

    Determine the required angular velocity $\omega$ of the relative position vector in order to maintain a constant separation distance $r_0$ for two equal masses. What equations are needed for this?
  8. B

    What is the Curl of the Position Vector?

    Homework Statement compute the curl of: \vec{r} and \frac{\vec{r}}{r^3}Homework Equations \vec{r}=x\hat{x}+y\hat{y}+z\hat{z} r^3=(x^2+y^2+z^2)^\frac{3}{2} The Attempt at a Solution I figured out that the curl of \vec{r} = 0 as my book says it should be... however...I also need to prove...
  9. M

    What is the significance of V(0) = -j in finding position vector?

    Problem: Find position vector given a(t) [ look in paint doc] v(0) = i, r(0) = j I highlighted a portion in the paint doc that I have a question for. Why V(0) = -j + C? = i? Where did they get the -j?? Thank you.
  10. P

    Kinematics in 2 dimensions; position vector problem.

    Homework Statement "A particle moves in the horizontal plane that contains the perpendicular unit vectors i and j. Initially it is at the origin and has velocity 18ims^-1. After accelerating for 10 seconds its velocity is (30i + 8j)ms^-1. Assume that the acceleration of the particle is...
  11. R

    Regualr hexagon and position vector - how does this work

    Homework Statement a regular hexagon OPQRST has its vertices at O ( the origin) and points P,Q,R, S,T with position vector p,q,r,s,t respectively. The point U with position vector u is the midpoint of the line segment OP, and SU meets OR at the point V please see attached diagem I need...
  12. M

    Position vector r and uncertainty principle

    Hi physicists, How can two atomic-scale particles interact through gravitation (Gm1m2/r^2) or any other force that is a function of r if r isn't know with complete certainty. Is it that the force itself also comprises uncertainty in its value? Thanks
  13. T

    Motion of a particle given position vector.

    Homework Statement A position vector of a particle at a time t is r=icost +jsint +kt ; show the speed and the magnitude of the acceleration is constant. Describe the motion. Homework Equations v = dr/dt a = dv/dt The Attempt at a Solution Could someone let me know if I am doing...
  14. Z

    Help Solving Calculus/Mechanics Question on Particle in Gravity Field

    I'm really struggling to get my head around some of the mechanics applications in my calculus module and would really appreciate it if somebody could help me get my head around it. I have this question: A particle P of constant mass m has a position vector: r=x(t)i+y(t)j, and moves...
  15. M

    Deduce primitive lattice vectors from position vector.

    Homework Statement given the following position vector: R = (10n1 + 9n2 + 19n3)(a/10) x + 6(n2+n3)(a/5) y + 2(n3)a z where n1, n2 and n3 are integers Find the primitive lattice vectors. Homework Equations any position vector of a lattice point is of the type R= c1 a1 + c2 a2 + c3 a3; and...
  16. N

    {vectors}find the position vector of this

    Homework Statement a particle traveling in a straight line is located at the point (4, -2, 3) with the speed of 2 m/s at time t=0. the particle moves toward the point (6, 0, 9) with constant acceleration 3i-j+k. find its position vector r(t) at time t The Attempt at a Solution...
  17. T

    Finding the Position of a Spaceship with Given Acceleration and Velocity Vectors

    Finding a position vector... Homework Statement A spaceship is traveling with acceleration a(t)=<e^(t) , t , sin2t>. At t=0, the spaceship was a origin r(0)=<0,0,0> and had an initial velocity of v(0)=<1,0,0> Find the position of the ship at t=piHomework Equations uhhh... The Attempt at a...
  18. L

    Finding the position vector of uniform circular motion

    Homework Statement Write an equation for one component of the position vector as a function of the radius of the circle and the angle the vector makes with one axis of your coordinate system. Calculate how that angle depends on time and the constant angular speed of the object moving in a...
  19. L

    Difference between Position Vector & Displacement Vector? (no calculatins)

    Difference between "Position Vector" & "Displacement Vector?" (no calculatins..) http://en.wikipedia.org/wiki/Position_(vector ) http://en.wikipedia.org/wiki/Displacement_(vector ) Is the position vector simply an initial vector given by coordinates (x,y) or (x,y,z) such as (8,4) or...
  20. E

    Converting Position Vector vs Time to Cartesian Coordinates

    1. The position vector of a particle at time t ≥ 0 is given by r = sin(t)*i + cos(2t)*j. Find the cartesian equation for the path of the particle. 2. I was told that the answer is: y = 1 - 2x^2 But I don't know how to obtain that solution. 3. r = sin(t)*i + cos(2t)*j At first I...
  21. B

    2d Motion, calculating time when v=0 from position vector

    Homework Statement The position vector of a particle is given by r= ihat(2t^3-21t^2+60t+10) +jhat(3/2)(t^2-10t+9) At what time, if any, is the velocity of the particle zero (ie what time is the particle instantaneously at rest) Homework Equations The Attempt at a Solution...
  22. D

    Calc 3/Vectors/Finding when object is furthest from origin given position vector.

    Hi guys I posted a picture of the problem set and my work so far. I am on letter (d) of the problem set and I am stuck. I am 90% sure I have the formulas to solve (d) through (g) but I am not clear how. Can anyone give me a basic idea on what step I should take next? Problem set my work...
  23. J

    The velocity and acceleration of particle give position vector

    the position vector of the particle is given by s=e^-2ti+sin(2t)j+5t^k calculate its velocity and acceleration at t=0 to get the velocity i differentiated with respect to t and substituted in t=0, giving me velocity=-2i+2j and that's the same as the answer given but I am not sure how to get...
  24. P

    Position vector perpendicular to tangent vector yields a sphere

    Homework Statement If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with center the origin. Homework Equations -1/r'(t)= slope of position vector x^{2}+y^{2}=1 The Attempt at a...
  25. D

    Finding minimum speed given position vector.

    Homework Statement r(t) = < t^2, 6t, t^2 − 24t > Using this position vector, find the minimum speed of the particle. Homework Equations v(t) = r'(t) The Attempt at a Solution I've found similar topics with similar problems but I'm having a hard time figure mine out. I know...
  26. Y

    How to verify a position vector points to a point inside a sphere?

    Homework Statement Given a sphere center at (2,2,2) with radius of 1.5, given a vector A=<3,2,1>. How do I verify A point to a point inside the sphere? Homework Equations Equation of circle: \sqrt{(x-2)^2+(y-2)^2+(z-2)^2}=1.5 The Attempt at a Solution I know A point to a...
  27. Y

    Confirm the characteristic of Position Vector.

    I want to confirm this, for any position vector. 1) They are radial vector that start from the origin to a point in space. 2) If A is a position vector: \nabla X \vec A \;=\; 0 \;\hbox { and }\; \nabla \cdot \vec A \;\hbox { not equal to zero. } 3) Any position vector in spherical...
  28. P

    Need help with integration position vector question

    Hi, can anyone help me with this question? Or give me some helpful links. I'm stuck! It's question B2 part b. Thanks.
  29. V

    Sperical coords: Position vector of spinning disk.

    I posted this in the Intro physics sections, but then realized that spherical coords might be a bit complex for introductory physics. This has been bothering my head for a couple days now. Any help is appreciated. Given: A wheel of radius R rotates with an angular velocity. The wheel lies in...
  30. V

    Position vector in spherical coordinates.

    I have not done this in a while and I am having a brain fart. Given: A wheel of radius R rotates with angular velocity Ct2 k\hat{} (lies in x-y plane, rotating about z). A point P on the circles is P(x,y,z) = (0,R,0) Ques: What is the position vector of point P in spherical coordinates...
  31. M

    Proving Magnitude of Position Vector for Centre of Mass

    Homework Statement Prove that the magnitude R of the position vector for the centre of mass from an arbitrary origin is given by the equation M2R2 = M\summiri2 - (1/2)\summimjrij2 Homework Equations F = MR'' F = p' p = \summjrj' The Attempt at a Solution I'm not...
  32. D

    Find the net force with the given position vector

    [b]1.The position vector of a 3000N helicopter is given by: r=(.02 m/(s^3))(t^3)i + (2.2m/s)tj - (0.06 m/(s^2))(t^2)k Find the net force on the helicopter at t = 5s. [b]2. I really have no clue where to begin. [b]3. I started doing this: r=...
  33. A

    How to determine Force from hor. position vector?

    Homework Statement An object with mass 5000 grams starts from rest and its motion is described by the horizontal position vector given. Determine the force acting on this object at the time t=9sec: x(t)=(.01/3)t^4-(.08sqrt(t^5)) Homework Equations F=ma The Attempt at a Solution...
  34. M

    Position vector of a moving particle (calc based intro)

    Homework Statement Reviewing for a midterm. I have this problem I can't seem to nail. Want to try it? "The acceleration of a particle moving only in a horizontal xy-plane is given by a=<(3t)i,(4t)j>, where 'a' is in m/s^2 and 't' is in seconds. At t=0, the position vector r=<(20)i,(40)j>...
  35. L

    Circular motion - determining expression for a position vector

    1. Consider a particle--the small red block in the figure--that is constrained to move in a circle of radius R. We can specify its position solely by theta(t), the angle that the vector from the origin to the block makes with our chosen reference axis at time t. Following the standard...
  36. S

    Find position vector from given velocity

    Homework Statement A particle A of mass m is traveling on a horizontal surface with velocity 7i-4j and collides with a stationary particle of mass 3m at the origin of the co-ordinate system at time t=0 Find an expression for the position vector of A at time t<0 NB: There is more to...
  37. V

    Velocity of a particle GIVEN position vector

    A [article follows the path given by the position vector r= (4t , 3 , t^3) what's its' speed at t=1? no idea how to solve this i know velocity is the derivative of the position with respect to time do i just solve, 4, 0, 3t^2, then stick it in? 4 + 3 = 7m/s??
  38. A

    How to determine position vector.

    Hi guys.I n moment,Im confused as to how to determine the signs that go next to the position vector.On what thing do they depend?Do we take the position vector from point of application of force to axis of rotation or otherwise?EDIT:If I am not being specific enough please say so guys.I really...
  39. M

    Position vector and tangent vector in Riemannian spaces

    In Euclidean vector spaces the derivative of the position vector of a running point of a curve is the tangent vector of the curve. In thehttp://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf" , on page 78 appears a vector which can be regarded as position vector in a Riemann space...
  40. X

    Position vector and magnitude problem

    Homework Statement A position vector in the first quadrant has an x-component of 6.0m and a magnitude of 10m What is the value of its y-component? Homework Equations ? The Attempt at a Solution Well I originally thought I could draw a graph where x=6 and y=...then I realized i...
  41. R

    How Do You Calculate the Position Vector of Point P in a Given Ratio?

    Homework Statement Use vectors to find the position vector of point P if P divides AB in the ratio 3:2 given A (-1,6,4) and B (4,1,-1) The Attempt at a Solution Well I assume it's sort of like finding the midpoint, except I would do something like (-1+4)/1.5 etc. Am I correct? Do I...
  42. S

    Calculate A, Distance, & Position Vector of T & S

    1. Given A = x^2y.ax — yz.ay + yz^2.az, determine: (a) The magnitude of A at point T(2, -1,3) (b) The distance vector from T to 5 if S is 5.6 units away from T and in the same direction as A at T (c) The position vector of S 3. (a) well for this one just plug in the point T, and...
  43. K

    What exactly is a position vector?

    What exactly is a position vector? Does a position vector ALWAYS have it's initial point at the origin (0,0)? What if there was an equivalent vector from P1 (NOT the origin) to P2 that has the same magnitude and direction as a vector with its initial point at the origin? Obviously these...
  44. K

    Proving 3 Non-Coplanar Vectors with Position Vector r

    Hi there, I'm a bit stuck on this question: " Given 3 non-coplanar vectors a, b and c convince yourself that the position vector r of any point in space may be represented by r = λa + μb + γc for some real numbers λ, μ and γ. Show that r.(bxc) = λa.(bxc) , r.(axb) = γa.(bxc)...
  45. A

    The Units of a Position Vector in a Hilly Landscape

    My problem is not so much the mathematics of doing the question, but rather the units. The question states: "A car travels across a hilly landscape with a position vector given in the x - z plane. Position Vector = 30 km/hti + 1 km cos (t/(0.1h))k How can the units for a position...
  46. C

    Position vector and velocity vector

    Hi everyone, Could someone please help me on this problem? Homework Statement A particle initially located at the origin has an acceleration of a=1.00jm/s^2 and an initial velocity of V=8.00im/s a. Find the position vector at any time t (where t is measured in seconds) b. Find the...
  47. K

    Position vector relation between comet and earth

    Homework Statement There is a comet that is at a position between the Earth and the sun that has an orbital radius half that of Earth's, this is the perihelion position for the comet. The comet's and Earth's orbits are coplanar. The comet's orbit crosses that of the earth's. When the comet...
  48. P

    Showing position vector follows parabolic path

    Homework Statement Hi, got my HW back from prof. There were a few problems... I want to understand these before the test. Show that r(t) = (at^2)/2 + vt + r lies in a plane and that if a and v are not parallel, then r(t) traces out a parabola. Note a, v, and r are constant vectors here...
  49. A

    Physics Lab - Projectile Motion - Deriving a Position Vector

    Homework Statement Okay, this lab has had me stumped for the last few hours. This is our first lab for AP Physics BC. Problem: Determine the position vector that describes the locatino of the water that is launched by a drinking fountain. Your position vector needs to be in unit vector...
  50. S

    Position Vector Help: Solve for t = 9.00 s

    The acceleration of a particle on a horizontal xy plane is given by a = 4t i + 5t j, where a is in meters per second-squared and t is in seconds. At t = 0, the particle has the position vector r = (20.0 m) i + (40.0 m) j and the velocity vector v = (5.00 m/s) i + (2.00 m/s) j. (a) What is the...
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