Position vector Definition and 109 Threads

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 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...