Unit vector Definition and 167 Threads

Homework Statement So the full problem reads: A vector F has the same magnitude and direction at all points in space. Choose the z-axis parallel to F. Then , in Cartesian coordinates, \vec{F}=F\hat{z}, where \hat{z} is the unit vector in the z direction. Express \vec{F} in spherical...

In the Feynman Lectures on Physics chapter 28, Feynman explains the radiation equation $$\vec{E}=\frac{-q}{4\pi\epsilon_0 c^2}\, \frac{d^2\hat{e}_{r'}}{dt^2}$$ The fact that the transverse component varies as ##\frac{1}{r}## seems fairly obvious to me since what matters is just the angle...

I think this is a textbook-style question, if I am wrong, please redirect me to the forum section where I should have posted this. This is my first time here, so I am sorry if I am messing it up. Homework Statement We have an n-dimensional vector \vec{r} with a constant length \|\vec{r}\|=1...

Homework Statement For the equations: y1 = 1-x^2 y2 = x^2 -1 find the unit tangent vectors to each curve at their point of intersection. Homework Equations d/dx (y1) = -2x d/dx (y2) = 2x The Attempt at a Solution After solving for points of intersection between the...

Homework Statement This is almost exactly the same problem as my earlier post, however different equation and point. Find the unit vector parallel to the graph f(x) = tan(x) and the point (pi/4 , 1) , and the unit vector perpendicular to the graph and point (pi/4 , 1 ). Homework...

Homework Statement Find the unit vector normal to the function f(x) = -3x^2 + 5 and the point (1,2) and find a unit vector parallel, using f(x) and the point (1,2). Homework Equations How do I find the slope here? I attempted to just use the point (0,5), and then the given point...

i came to this topic and they said Duf(x) = ||gradient vector|| * ||U|| * cos 0 if ||U|| were not a unit vector it would give different rate of change of f in any direction what would happens if used ||U|| = 10 ?

Homework Statement I am trying to calculate the flux for the octant of a sphere, and I am trying to figure out how the mathematics, dot products, and dA works in the integral. I already did the quadrant for \hat{θ} where θ= π/2 (the bottom quadrant) and I did the left quadrant where \hat{n}...

In my textbook, it states that given q1 and q2 where both charges are positive and of equal magnitude, the unit vector r-hat always points away from q1. Why is this so? What if both charges are of opposite charge? Does r-hat still points away?

I have the following question: Given that ø = (x^2)y + cos(z) find the unit vector n which is both tangent to the surface of constant ø at (1,1,∏/2) and normal to the vector b = x + y - 2z (where x y and z are the unit vectors) I have calculated ∇ø = 2x + y - z (again where x y and z are...

Hi everyone, I've two vectors in cylindrical coordinate - (-1,\frac{3\pi}{2},0),(2,\pi,1) - and I want to find the perpendicular unit vector of these two vector. Basically I'll use the cross product, then I'll find the unit vector by \hat{u}=\frac{\vec{u}}{||\vec{u}||}. But do you I...

Homework Statement You are given that with x = (x1,x2), y = (y1,y2), the formula (x,y) = [x1 x2] [2 1;1 2] [y1;y2] (where ; represents a new row). is a inner product for the vectors in R2 Using this inner product, find a unit vector perpendicular to the vector (1,1) Homework Equations The...

Homework Statement When a vector A is dotted with a unit vector, the result is... Select one: a. zero b. the magnitude of the unit vector in the direction of A. c. the magnitude of A. d. the angle between A and the unit vector. e. the magnitude of A in the direction of the unit vector...

Homework Statement Say for example, a particles velocity was given by the following equation: \vec{V}[SIZE="3"](t) =[SIZE="3"] (2t2-4t3)\hat{i} - (6t +3)\hat{j} + 6\hat{k} If I wanted to find the displacement of the particle between t=1s and t=3s, could I just integrate like this...

Before anyone thinks I didn't numerous attempts before opening this topic, take a look at my rough draft of mathematics in the annex. So, a simple question. How derivate an unit vector wrt any variable? I can derivate any unit vector wrt θ or φ, obivious, but how derivate the vector φ wrt to x...

Homework Statement the first derivative of a vector of constant magnitude is the cross product of the angular velocity of the vector(i.e , the angular velocity of the moving coordinate system ) and the vector itself.)Homework Equations di/dt= w x i , here w is the angular velocity and x is...

As a particle orbits around a circle, the unit vector of the velocity and acceleration component is constantly changing, so, how do I determine the unit vector?

Homework Statement I have a problem that is the curl of jln(rsinθ) Since this is in spherical, why is there a bold j in the problem? Doesn't that indicate it's a unit vector in cartesian coordinates? Can I do the curl in spherical coordinates when I have a cartesian unit vector in the...

Given a trapezium ABCD with AB parallel to CD. Show that the line joining the midpoints of the diagonals is parallel to AB & CD (done). Show also that its length is the difference of AB and CD. working: I called the midpoint of AC, E and the midpoint of BD, F Then found that ##...

Homework Statement A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the...

Homework Statement The vector -i+j+k bisects the angle between the vector c and 3i+4j. Determine a unit vector along c. Homework Equations The Attempt at a Solution Taking the dot product of the two vectors (other than c) gives me the cosine of the angle = 1/5√3. This is also equal...

i have a problem : A small loop antenna in free space and centered about the origin on the xy-plane is producing a (far-field) radiation electric field (in phasor notation) : http://postimg.org/image/63tm76h5l/ and their solution : http://postimg.org/image/6mdm6roh9/ i don't understand how...

I want to find the unit vector of ## \vec E= \hat x A\;+\;\hat y Be^{j\phi}## ##\hat E=\frac {\vec E}{|\vec E|}## From my work: ##|\vec E|=\sqrt{A^2+(Be^{j\phi})^2}## My question is what is ##(Be^{j\phi})^2##? Do I substitude ##e^{j\phi}=\cos \phi +j\sin \phi##? So...

Homework Statement The problem states to find a unit vector that is orthogonal to \left\langle1, 1, -2\right\rangle, forms an angle of \frac{\pi}{4} with \left\langle1, 1, 1\right\rangle and has v1 > 0. Homework Equations cos\theta = \frac{\vec{u}\bullet\vec{v}}{|\vec{u}||\vec{v}|}...

Homework Statement Not sure if this belongs in homework or general discussion - I found this in reading In studying the divergence and curl of the magnetic field (B), I found a statement that I need some help with. In the derivation of the divergence of B using the Biot-Savart, I have...

OK, I'm really rusty on this. I need to convert a unit vector to right ascension and declination. I believe I recall the formulae correctly, as I seem to have gotten 1 as my radius. So, that's good. In the pic I have my unit vector (P2), my actual answer below, my expected answer in...

Hi guys, I've run across a problem. In finding the potential energy between two electrical quadrupoles, I've come across the expression for the energy as follows: U_{Q}=\frac{3Q_{0}}{4r^{4}}\left[(\hat{k}\cdot \nabla)(5(\hat{k}\cdot \hat{r})^3-2(\hat{k}\cdot \hat{r})^2-(\hat{k}\cdot...

Homework Statement http://i.imgur.com/B1hFY6E.png Homework Equations -Basic geometry -Similar triangles (?) -Pythagorean Theorem The Attempt at a Solution -I need to find the angle the bar AB makes with the horizontal, correct? And with that, I will be able to figure out the...

Homework Statement http://prntscr.com/p7dxt Here's a screenshot of the revision question. Homework Equations The Attempt at a Solution Co-ordinates of each point A, (0, 60, 0) B, (40, 0, 0) C, (-40, 0, 40) D, (-60, 0, -60) Position Vectors rAB, 40i + -60j + 0k rAC, -40i + -60j + 40k rAD...

Hi all! I must compute a derivative with respect to the components of a unit vector \hat{p}^{i}. In spherical coordinates, \hat{p}^{1}=\hat{p}^{1}(\theta,\phi)=\cos\theta \sin\phi I want to express the derivative \frac{\partial}{\partial\hat{p}^1} as a combination of...

Homework Statement Express the 5.2-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA. I have attached an image of the problem. Homework Equations Fx = Fcos(θ) Fy = Fcos(θ) Fz = Fcos(θ)...

Homework Statement Let r=(x,y,z). Find ∇r(hat). Homework Equations r(hat)= (x,y,z)/sqrt (x^2+y^2+z^2) ∇f=df/dx x + df/dy y... The Attempt at a Solution Okay I'm having a complete brain freeze at the moment. I know the denominator is a magnitude but am I still supposed to use the...

Homework Statement Find all values of a such that w=ai+\frac{a}{8}j is a unit vector. Homework Equations unit vector has length of 1. and for a vector v unit vectors would be v/magv The Attempt at a Solution 1=magw=\sqrt (a2+(a/8)2) 1=a2+(a2/64) 64=2a2 32=a2 a=\sqrt{32} i know...

I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!

Say for example v = <3,4> I was taught to divide each component by the magnitude in order to get the unit vector, i.e. 3^2 + 4^2 = ||v||^2 5 = ||v|| So the unit vector of that vector is <3/5,4/5> or 1/5<3,4> But if I forgot that I had to divide the components by the magnitude, I would not...

Our teacher taught us a way to represent a force as a unit vector. Suppose a force of 12 N acts along the line 2i+j-2k. The force is written as: F = 12 N (2i+j-2k/√1^2+2^2+2^2) Therefore, F = 8i+4j-8k But, I can't understand why is it so. Please explain.

Homework Statement Given vector OP = 2i+3j, OQ = qi+2qj. How can i find the possible value for q? note that PQ is a unit vector. Homework Equations Given (p-1)i + (2p-6)j having magnitude 10, find p The Attempt at a Solution From the formula, i was told that the unit vector...

hey, i've been trying to work out how to determine the sign of cross products of unit vectors, for example in cylindrical, r x z = - theta theta x z = r r x theta = z i can't figure out the sign, r x z = |r||z|sinβ theta where β is the angle between them, which is 90°...

Homework Statement Let c(t) be a path of class C1. Suppose that ||c(t)||>0 for all t. Show that c(t) dot product with d/dt((c(t))/||c(t)||) =0 for every t. Homework Equations I am having trouble with the derivative of (c(t)/||c(t)||) and how to show that when its dotted with c(t) that...

If you already have one of the two coordinates?

Find unit vector with a given angle to two other vectors in 3-space Homework Statement We are given the vectors <1,0,-1> and <0,1,1>, and are told to find a unit vector that shares an angle of (pi/3) with both of these vectors. Homework Equations a(dot)b = |a||b|cosθ The...

Homework Statement If u is a unit vector, find u.v and u.wHomework Equations I assumed that unit vector means u=<1,1,1> u.v=|u||v|cos60 My knowledge of unit vectors is very limited. I know that a unit vector is i=<1,0,0> j=<0,1,0> k=<0,0,1> The Attempt at a Solution Since the triangle is...

Homework Statement Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8). Homework Equations u = PQ = Q - P v = PR = R - P ans = uXv = PQ X PR The Attempt at a Solution so I did...

Find the unit vector that makes an angle θ=-3∏/4 with the positive x-axis I know to find a unit vector you divide the given vector by its magnitude, so I guess my problem is finding any vector that makes that angle with the positive x axis. I figured if that angle was the slope of a line, then...

Homework Statement Prove that the unit vector r{hat} of two-dimensional polar coordinates is equal to r{hat}= x{hat}cosθ + y{hat}sinθ and find the corresponding expression for θ{hat}. all I need is the last part... I'm just not sure what θ{hat} is? How do I go about doing this? Nothing in my...

Let be w=w(σ) a curve on a surface parametrized by the arc length (the natural parametrization). Consider the m surface normal along this curve as the function of the σ arc length of the curve. Prove that m'(σ) is parallel to the t(σ) tangent unit vector of the curve for all σ, IFF this curve is...

Let us say there is a curved region of spacetime whose curvature is \kappa(s). How does one find the coordinates of the unit vector normal to a certain point on the region of spacetime? I tried searching Hamilton's principle and the general theory of relativity but I could not find any equation...

Homework Statement Suppose f is a smooth function of x and y, and at the point (1,1), \partialf/\partialx = 1, \partialf/\partialy = -1. Find the unit vector u such that Duf(1,1) = 0 Homework Equations Duf(1,1) = \nablaf(1,1) * u = 0 The Attempt at a Solution My answer was...

Homework Statement Two vectors are given by the relations a = 2i-3j-3k b = 6i+2j+k Find unit vectors corresponding to a 3- dimensional orthogonal right handed coordinate system where one of the axes is parallel to _{}a and another of the axes is perpendicular to _{}b Homework...

Homework Statement use unit vectors to express the vector C where C=3.00A-4.00B the answer is apparently C=12.0i + 14.9j Homework Equations cross product The Attempt at a Solution i have no idea where to even start how is it possible to find the i orj because i don't even know...