Vector notation Definition and 66 Threads

Homework Statement PART A: A force ~F = Fx ˆı+Fy ˆ acts on a particle that undergoes a displacement of ~s = sx ˆı + sy ˆ where Fx = 6 N, Fy = −3 N, sx = 5 m, and sy = 1 m. Find the work done by the force on the particle. Answer in units of J. PART B: Find the angle between ~F and...

Afternoon, I'm studying Engineering Dynamics (4th Year Undergraduate) and I was wondering if anyone can point me to a resource with regards to rotating reference frames and vector notation? The notes I've been given aren't particularly helpful. Much appreciated.

Unit Vector notation?? The vector position of a particle varies in time according to the expression r = (3.0i +6.0j)m Find expressions for velocity and acceleration as functions of time. I have NO IDEA HOW TO DO THIS.

The arc length of a circle is radius times the angle between the two radius legs that connect the arc. Thus dL = R d@ and dF = I dL x B where B and dL and dF are vectors. how can I convert dL = R d@ into vector notation so that I can simplify these two expressions??

Hello everyone! I am trying to do a literature search about ion scattering spectroscopy experiments. But I am not good at the vector notation which is used in these articles. I mean the notations with square brackets like [11-2] or [1-10] etc. (-2: the bar is on 2). For instance in a graph like...

i don't have a problem just a little confusion. what exactly does the i hat and j hat notation mean when given a vector problem. such as \vec{}a= 0.023 \hat{}im/s^{}2 + 0.046 \hat{}jm/s^{}2 what is this statement actually saying. i know what i need to do with it, but don't quite grasp...

Homework Statement An electron has an initial velocity with an x component of zero, a y component of 17.2 km/s, a z component 20.7 km/s, and a constant acceleration of 1.95 x 1012 m/s2 in the positive x direction in a region in which uniform electric and magnetic fields are present. If the...

Homework Statement if \phi = rk/r^{3} where r=xi + yJ + zk and r is the magnitude of r, prove that \nabla\phi = (1/r^{}5)(r^{}2k-3(r.k)r Right I'm not really sure where to start here... i know Magnitude r = \sqrt{x^{2}+y^{2}+z^{2}}

wave equation -- vector notation what does the solution to the SE look like if expressed in vector notation? say if we just used phi as a function of x and t.

[SOLVED] vector notation and force and force Help- test this morning.. Homework Statement A time dependent force F(t)= 20t N/s acts along the possitive y-axis on a 4.00kg object. The object starts at the origin with the initial velocity \vec{}v(0)= (1.00m/s)) \hat{}i-(1.00m/s) \hat{}j...

Homework Statement a. How do I write vectors bold within displaymath and frac. I want Phi, r and r_1 bold. But get G M_1 bold as well = bad. b. How do I use arrows instead of the bold notation? The Attempt at a Solution \begin{displaymath} a1. textbf{\Phi(r)} = -\frac{G M_1}{|...

Homework Statement Vector a1 + vector a2 = 5*vector a3 Vector a1 - vector a2 = 3*vector a3 Vector a3 = 2i + 2j (i and j are the vector components) Express 1) vector a1 and 2) vector a2 in unit vector notation Homework Equations Vector R = Ax + Yx The Attempt at a Solution I took the first...

Homework Statement Vector a1 + vector a2 = 5*vector a3 Vector a1 - vector 12 = 3*vector a3 Vector a3 = 2i + 2j (i and j are the vector components) Express 1) vector a1 and 2) vector a2 in unit vector notation Homework Equations Vector R = Ax + Yx The Attempt at a Solution I...

I've got an equation (from Wikipedia)for the electrostatic potential of an electric dipole. It looks like this: \Phi (\mathbf{r}) = \frac {1} {4\pi\epsilon_0 r^2} (\mathbf{p}\cdot\hat{\mathbf{r}}) E is the electric field r, r, r\hat are as above p is the (vector) dipole...

In Figure 13-34, a square of edge length 21.0 cm is formed by four spheres of masses m1 = 6.00 g, m2 = 3.00 g, m3 = 1.00 g, and m4 = 6.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.40 g? Well by using Newton's Law of...

I am having a hard time with this problem, and i need some help. It says: In Exercisies 11-17, use set theoretic or vector notation or both to describe the points that lie in the given configurations. 11.) The plane spanned by v1 = (2,7,0) and v2 = (0,2,7) In the back of the book they...