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.
Homework Statement
suppose that grad of f(x,y,z) is always parallel to the position vector xi+yj+zk. show that f(0,0,a)=f(0,0,-a) for any a.
The Attempt at a Solution
grad of f= fx(x,y,z)i+fy(x,y,z)j+fz(x,y,z)k ; then gradf (dot) pos.vector = |gradf|*|pos.vector| (since cos(teta)=1 )...
Homework Statement
Suppose that the position function of a spaceship is r(t) = (3+t)i + (2+ln T)j + (7-4/t^2+1)k. Suppose you want the ship to coast to a space station located at (6.4.9). What time should you turn your engine off?
Homework Equations
r' = velocity. r" = acceleration...
Homework Statement
The position function of a spaceship is
r(t) = (3+t)i + (2+ln t)j + (7 - 4/(t^2+1)k and the coordinates of the space station are (6,4,9). If the spaceship were to "coast" into the space station, when should the engines be turned off?
Homework Equations
The...
can anyone help me with this question:
A sphere of unit radius is centered at the origin. points U,V & W on the surface of the sphere have vectors u,v & w. find the position vector of points P&Q on a diameter perp to the plane containing points U,V & W?
can anyone help
I was wondering, why does the position vector always points radially out from the center (for example, in circular motion). I figure that this is because \vec{v} = \frac{d \vec{r}}{dt} and the velocity should always be tangent to the "curve" (because of Newton's first law).
But is there any...
3. A tennis ball is served horizontally from 2.4 m above the ground at 30m/sec
a) Find its velocity (V) at any time t seconds
b) Find its position vector (r) at any time t second
a) v= 30i - gtj
b) i integrated and got position vector as
p= 30ti(2.4-.5gt^2)j
is that it?
it is said that the posiion vector of the cener of mass of a rigid body can be obtained by:
r_{CM}= \frac{1}{M} \int r dm
I'm not sure I understand this expression. What exactly is dm? and I thought it was the sumation of mass times distance divided by the total mass...
A particle has position vector 2i + j (i is along x-axis and j is along y axis) initially. and is moving with speed of 10m/s in the direction 3i-4j. Find its position vector when t=3 and the distance it has travlled in those 3 seconds.
Please help me with the first part of the question. :confused:
I have been struggling with this question for a little while now and after drawing pictures and such I just cannot think of a situation in which this is possible. I was wondering if somebody with a little bit more physics knowledge could enlighten me :rolleyes: ? Here it is:
"Describe a...
Let \vec{r} = \vec{r}(q_1,\ldots,q_n) .
Is the following ALWAYS true?
\frac{\partial \vec{r}}{\partial q_i} \cdot \frac{\partial \vec{r}}{\partial q_j} = \delta_{ij}
Edit: Perhaps I should ask if it is zero when i \neq j rather than saying that it is 1 when i = j
I guess...