Vectors Definition and 1000 Threads

Homework Statement https://www.dropbox.com/s/8l90hahznjlv9d0/vector%20problem.png?dl=0 Homework Equations Dot and Cross product The Attempt at a Solution although I know the dot and cross product, I'm not sure what I'm being asked or how to proceed? any help?[/B]

I'm having trouble understanding those concepts in the title. Can someone explain those concepts in an easy to understand manner? Please don't refer me to a wikipedia page. I know some linear algebra and multi-variable calculus. Thank you.

Hi all. I'm struggling with taking dot products between vectors in spherical coordinates. I just cannot figure out how to take the dot product between two arbitrary spherical-coordinate vectors ##\bf{v_1}## centered in ##(r_1,\theta_1,\phi_1)## and ##\bf{v_2}## centered in...

Homework Statement From Kleppner and Kolenkow Chapter 1 (Just checking to see if I'm right) Given vector A=<3, 4, -4> a) Find a unit vector B that lies in the x-y plane and is perpendicular to A. b) Find a unit vector C that is perpendicular to both A and B. c)Show that A is perpendicular to...

Homework Statement Vector A lies in the yz plane 65.0° from the positive direction of the y axis, has a positive z component, and has magnitude 5.10 m. Vector B lies in the xz plane 42.0° from the positive direction of the x axis, has a positive z component, and has magnitude 1.70 m. Find (a)...

Homework Statement (f) At t = 0, a particle of mass m trapped in an infinite square well of width L is in a superposition of the first excited state and the fifth excited state, ψs(x, 0) = A (3φ1(x) − 2iφ5(x)) , where the φn(x) are correctly-normalized energy eigenstates with energies En. Which...

So I know that the basis vectors of an FCC in a symmetric form are: a = \frac{a}{2}(\hat{x} + \hat{y}) b = \frac{a}{2}(\hat{y} + \hat{z}) c = \frac{a}{2}(\hat{x} + \hat{z}) And that the reciprocal lattice vectors are the basis vectors of the BCC cells. I'm having a hard time doing the...

How would I go about setting up a Biot and Savart Integral using Vectors? Here is an exercise we had in class: I tried to set it up using Vectors, and figured dl to be <-L,L> and r to be <½L, -½L>. After the cross product, I am not sure how to handle the integration, since r can vary. Would...

Homework Statement Three vectors, A, B and C each have a magnitude of 50 units. Their directions relative to the positive direction of the x-axis are 20°, 160° and 270°, respectively. Calculate the magnitude and direction of each of the following vectors. a)[/B]→A+ →B+ →C b)→A− →B+ →C c)2 (...

Homework Statement In the arrangement as shown in the figure below, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. Mass M moves upward with a speed: a. 2ucosθ b. u/cosθ c. 2u/cosθ d. ucosθ Homework Equations None, I am not sure...

Homework Statement ## L (v^2 + 2 \pmb{v} \cdot \pmb{ \epsilon } ~ + \pmb{ \epsilon} ^2)##, where ## \pmb{\epsilon}## is infinitesimal and ##\pmb{v}## is a constant vector (## v^2 ## here means ## \pmb{v} \cdot \pmb{v} ## ), must be expanded in terms of powers of ## \pmb{\epsilon} ## to give...

I was going through this link -...

A car travels 10 km due EAST then 12. Km NW what is Magnitude of the car's displacement. The answer that I got in my book is 8.8 Could anyone-please-explain ?The Attempt at a Solution 6.6 km[/B]

Homework Statement Hi all, It is a homework problem, but I really don't quite understand the question. It reads- "3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, taken in order. Find their resultant"Homework EquationsThe Attempt...

Homework Statement Homework Equations - The Attempt at a Solution I know that the acceleration is downward always with value of 10m/s2 The answer is D? because j denote vertical axis and negative sign means downward? [/B]

I understand that Contravariant vectors have an upper index and co-variant vectors use a lower index. But why is one preferred over another in a specific physical situation? I am just struggling with which form is preferred, and why one would bother trying to raise or lower the index in a...

Homework Statement A machine carries a 4.0 kg package from an initial position of di=0.6m##\hat i## + 0.7m##\hat j## + 0.26m##\hat k## at t = 0 to a final position of df= 11.5m##\hat i## + 14.0m##\hat j## + 10.2m##\hat k## at t = 15.0 s. The constant force applied by the machine on the package...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] Hello, I have a problem with rotation matrices, its just a comparison problem. Θ must be 240 or -120, I don't know how the book show the answer like that, these are the two matrices...

Hello, Here's the problem: Suppose we orient the x-axis of a two-dimensional coordinate system along the beach at Waikiki. Waves approaching the beach have a velocity relative to thTe shore given by v = (1.3 m/s)y. Surfers move more rapidly than the waves, but at an angle to the beach. The...

Suppose the vectors ##v_a## and ##v_b## are linearly independent, another vector ##v_c## is linearly dependent to both ##v_a## and ##v_b##. Now if I form a new vector ##v_d##, where ##v_d = v_b+cv_c## with ##c## a constant, will ##v_d## be linearly independent to ##v_a##? I need to check how I...

Hey, all. I have a question concerning the treatment and use of vectors when solving problems (or in general, really). I know that vectors have both magnitude and direction, while scalars only have magnitude. However, in solving problems and looking at how others have solved them, I've noticed...

I was reading about the tangent vector at a point on a curve. It is formulated as r' = Lim Δt→0 [r(t+Δt) - r(t)] / Δt (sorry for the misrepresentation of the 'Lim Δt→0 ') where r(t) is a position vector to the curve and t is a parameter and r' is the derivative of r(t). All I can...

Homework Statement Particle X moves with a velocity of 15 m/s[R]. Particle Y moves with a velocity of 5.0 m/s[L]. What is the velocity of particle X with reference to particle Y? The correct answer is 20 m/s (R). I do not understand what velocity in reference to particle Y means, and how to...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] In textbook I am troubling understanding the question.Actually I don't know the terms ##\vec{u}_r## and ##\vec{u}_θ## Here the question. A particle moves according to the polar equation...

Hi, I'm internested in a good book that teaches vectors (and perhaps tensors?) so i can better understand books on classical/Newtoniam mechanics. I know the basics of vectors, but i still get confused when i se them in physics books and don't completely understand what's going on when physics...

Homework Statement Let ##u_1,u_2,u_3## be a basis and let ##v_1=-u_1+u_2-u_3## , ## v_2=u_1+2u_2-u_3## , ##v_3=2u_1+u_3## show that ##v_1,v_2,v_3## is a basis and find the components of ##a=2u_1-u_3## in terms of ##v_1,v_2,v_3## Homework Equations For basis vecor...

Homework Statement Find a vector in the direction opposite to <-4,1,2>, that has a magnitude of 3. Homework Equations I think that I did the first part of the problem correctly: <-4,1,2> magnitude= sqrt[ (-4)^2+1^2+2^2 ] = sqrt(16+1+4) = sqrt(21)...

Homework Statement I am having difficulty understanding the very first step of the following solved problem (I understand the rest of the solution). How did they obtain the expressions for ##\hat{n}## (the direction of polarization), and ##\hat{k}## (the unit vector pointing in the direction...

Homework Statement Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed...

Homework Statement Vectors A and B both have magnitude M. Joined at the tails, they create a 30' angle. What is A x B in terms of M? Homework EquationsThe Attempt at a Solution 0? OR M^2? Sqrt(3)M/3?

If two physical quantities are being multiplied , is there any way to know that the result will be a scalar of vector.. Moreover if two vectors are being multiplied how can we know that we have to apply cross or dot product??

The tangential velocity of a body rotating about the centre point "O" is given by v=w.r, where w is angular velocity and r = radius. give that the vectors w = 3i - 2j + 7k r = 2i + 5j - 3k a) Calculate the magnitude of velocity b) the vector product in the form i+j+k So far I have the vector...

Homework Statement [/B] Find points P,Q which are closest possible with P lying on the line x=8+1t y=8+1t z=7−3t and Q lying on the line x=231−6t y=−10−17t z=71−13t 3. Attempt at solution Hi, I am at loss as to how to do this. I know that from the equations I can get point (8,8,7) and...

Homework Statement Given that the primitive basis vectors of a lattice are ##\mathbf{a} = \frac{a}{2}(\mathbf{i}+\mathbf{j})##, ##\mathbf{b} = \frac{a}{2}(\mathbf{j}+\mathbf{k})##, ##\mathbf{c} = \frac{a}{2}(\mathbf{k}+\mathbf{i})##, where ##\mathbf{i}##, ##\mathbf{j}##, and ##\mathbf{k}## are...

Homework Statement For f(x,y)=x^2-xy+y^2 and the vector u=i+j. ii)Find two unit vectors such D_vf=0 Homework Equations N/A. The Attempt at a Solution Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum...

Hello I am a mechanical engineer who is teaching himself the math of exterior algebra and differential forms. It is not easy for me and I have had many SIMPLE stumbling blocks due to my not respecting algebra. May I ask for help on some simple aspects? (Please be patient with me.) My...

Consider the flat FRW metric in Cartesian spatial co-moving co-ordinates: ##ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2)## As I understand it, since the metric does not depend on the the spatial co-ordinates, there exist Killing vectors in the ##x##,##y##,##z## directions. Does this imply that the...

Suppose I have already found the surface normal vectors to a set of points (x,y), how do I compute the surface height z(x,y)? Basically what I have are the normal vectors at each point (x,y) on a square grid. Then I calculate the vectors u = (x+1,y,z(x+1,y)) - (x,y,z(x,y)) and v =...

The question suggests that r(t) = (x(t),y(t),z(t)) is a position vector along some curve where t goes from negative to positive infinity. Now suppose t has been chosen so that 1 = the dot product of dr/dt and dr/dt. Show that 0 = the dot product of dr/dt and d^2r/dt^2. I have attempted to...

At the moment we are working through problems in Griffiths' Electrodynamics textbook and it got me thinking... In magnetostatics we have the magnetic vector potential A and in the use of dielectrics problems we have the vector D. Why is it advantageous to use these vectors and not just stick to...

Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...

hello The below structure (the triangle) is connected to fixed point A that is a hinge (can rotate freely). Fc force is perpendicular to (ac) and Fb is horizontal. If the (bac) angle is 30 degrees, calculate the reaction at A. My attempt: Since Fc is perpendicular to (ac) it doesn't apply any...

If you know the position vectors of a particle at two points along its path, change in time between the two positions, and the particle's velocity at the earlier point, what quantities can you calculate? a)average acceleration b)final velocity c)average velocity d)displacement My answer was...

Homework Statement If the vectors a and b are non-collinear and the vectors c = (x-2)a + b and d = ( 2x + 1)a - b , are collinear then x is equal to Homework Equations c x d = |c| |d| sin θ n where n is unit vector The Attempt at a Solution Since c and d are collinear there cross product...

The way I understand it, they both have rectangular forms which are easy for addition/subtraction. Now I realize that the polar form of a complex vector can be simplified into an exponential, which is ideal for multiplication/division. But this is what confuses me; vectors don't multiply/divide...

Hi there, In the decay of ## B \to D^* l \nu ##, I found that the polarization vectors are described as following: In the B rest frame the helicity basis ## \bar{\epsilon}(0)= \frac{1}{\sqrt{q^2}} (p_{D^*},0,0,-q_0), \\ \bar{\epsilon}(\pm)=\pm \frac{1}{\sqrt{2}} (0,\pm 1,- i,0), \\...

Homework Statement Prove that if in a system of vectors: S_a =\{a_1, a_2, ..., a_n\} every vector a_i is a linear combination of a system of vectors: S_b = \{b_1, b_2, ..., b_m\}, then \mathrm{span}(S_a)\subseteq \mathrm{span}(S_b) Homework EquationsThe Attempt at a Solution We know due to...

Homework Statement [/B] This problem is from Jon Rogawski's Calculus-Early Transcendentals At a certain moment, a moving particle has velocity v={2,2,-1} and a={0,4,3}. Find T, N and the decomposition of a into tangential and normal components.Homework Equations ANYTHING IN [ ] REPRESENTS A...

If ##\sigma## is an affine paramter, then the only freedom of choice we have to specify another affine parameter is ##a\sigma+b##, a,b constants. [1] For the tangent vector, ##\xi^{a}=dx^{a}/du##, along some curve parameterized by ##u## My book says that ' if ##\xi^{a}\xi_{a}\neq 0##, then by...

I was asked to draw a free body diagram to derive the equation tan θ = µs for the following situation: A box sliding down an inclined plane. My FBD has 3 forces - gravitational forces pointing downward (horizontally) <-- longest vector - normal force perpendicular to the box - frictional...