Cross Definition and 1000 Threads

Homework Statement This isn't so much a problem of calculation, so much as it is I need to know if i did it right, you'll see what I mean. vectors v=(2,0,2), u=(-1,1,0), w=(0,-1,1) Computer the quantities that make sense (a period denotes the dot product, x denotes cross product)...

Can anyone help me with this calculus problem? I have tried it a couple of different ways, but keep getting various incorrect answers; I think my problem is probably in the setup. I am trying to find the volume of the solid created by revolving the area bounded by these two equations y = 6 -...

If A\in O(3) and v,w\in\mathbb{R}^3, then (Av)\times (Aw) = (\textrm{det}\;A) A(v\times w) is right, right? Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?

Homework Statement I need to calculate Ax(BxC) -A, B, C are vectors, apart from bac-cab rule, I need to get it by epsilon ijk -Following I will note it by e(ijk). Homework Equations I expect answerer to know kronecker delta equation and vector multiplications. The Attempt at a...

How do you prove that ||VxU|| is the area of the parallelegram they form? I know that the cross product is a vector perpendicular to V and U

Homework Statement How would you figure out the genotypes and phneotypes if you Cross TTBbRr with TtbbRr? Trihybrid cross Homework Equations Cross TTBbRr with TtbbRr The Attempt at a Solution I did the crossing, but i don't know how to do the genotypes nor the...

Not so much an actual problem, more like concepts. What exactly is the dot product? How about the cross product?

Homework Statement In the attached file, I need some help with questions 3 and 4. Homework Equations The Attempt at a Solution For question 4, I get the next answers: a. The flux is given by: f=\frac{v_{\nu}\rho}{m} where m is the mass of the iron nucleus, rho is the iron...

I am reading through David Widder's Advanced Calculus and he abbreviates a determinant as: \left( \begin{array}{cccc} r_{1} \ s_{1} \ t_{1}\\ r_{2} \ s_{2} \ t_{2}\\ r_{3} \ s_{3} \ t_{3}\\ \end{array} \right) And refers to it by (rst). He then states...

Yo guys, I was wondering: Why does the cross product of two vectors produce a third vector which is perpendicular to both the original vectors? I've come across it in math and it's one of those things I've accepted... but I'm not quite sure why it happens.

Homework Statement I have came up with an example to illustrate my question. There is a rod, which can turn around p1. p1p2 = (-1+j) m p1p3 = (-3 + 3j) m p1p4 = (1 - j ) m F1 = (1+3j) N F3 = (-1 - 2j ) N F4 = unknown, orthogonal to the rod compute F2_n, orthogonal component of F2 to the...

Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...

Homework Statement I need to find the volume of the solid generated by revolving this region bounded by the curves about the x-axis. y = sqrt(x), x+y=6, y=1 Homework Equations The Attempt at a Solution I find the intersections of these curves I get: (1,1), (4,2)...

Homework Statement C= B|A| + A|B| D= A|B|-B|A| C and D are orthogonal Find a third vector perpendicular to both C and D Homework Equations [AxB] = |A||B|sin(theta) The Attempt at a Solution I know that to find the answer I need to find the cross product of C and D. I have done...

Homework Statement I need to prove the identity div (a x b) = b dot (curl a) - a dot (curl b) The Attempt at a Solution I've done the proof about 10 times now, and everytime I get the left hand of the identity equal to this: (all the d's are partial derivatives) d(a3b1)/dx -...

Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio between cross products. Please tell me if the following makes sense. Say we have cartesian coordinates (x,y) and polar coordinates (\rho, \phi). I want to calculate...

The Rutherford differential cross section \frac{d\sigma}{d\Omega} goes like cosec(\vartheta)^4 which means at \vartheta=0 the differential cross section is infinite, which is ok. My question is, given that the differential cross section is proportional to the probability per unit solid...

What is significance of the trig functions in both the cross and the dot product? I understand what the dot and cross products are, how they work, and what they give...but I don't understand why the dot product uses cosine and the cross product uses sine?

This question has a few parts. r = i + 2j + 3k s = 2i - 2j - 5k t = i - 3j - k Evaluate: a)(r.t)s - (s.t)r b)(r x s) x t. deduce that (r.t)s - (s.t)r = (r x s) x t can you prove this relative true for any three vectors a)(r.t)s - (s.t)r (r.t)s well I don't know...

Is there any physical meaning to the cross product of two magnetic fields e.g. two fields generated in two different current loops?

My professor told me that the neutrons in a reactor see the surface area of nuclei, and not the the projected cross section. That really doesn't make intuitive sense. Is he right?

i know that τ=VQ/(Ib) now I am looking for the maximum stress so i will find that at the point at the centre of the rectangle Q=A*\bar{y} A=0.5*d*b \bar{y}=0.25*d ===> Q=0.125d2b I=(b*d3)/12 τ=VQ/(Ib) τ=V*0.125d2b*12/((b2*d3) τ=1.5V/(bd) now d changes as a function...

I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!

in a given shaft with a circular cross section, the radius changes linearly find the maximum shear stress i used T*r/J and since J is dependant on r^4, i found that the cross section with the smallest radius will feel the largest stress. find the angle of twist at the end of the...

Hello! I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle) yields the same value no matter which 2 adjacent sides are chosen. How would you prove mathematically that this is the case?

In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ? Cross product or dot product?

A 3.5 m long steel member with a W310 x 143 cross- section is subjected to 4.5KNm torque. Knowing that G=77GPa, determine (a) the maximum shearing stress along the line a-a, (b) the maximum shearing stress along the line b-b, (c) the angle of twist...

A and B are two hermitian vector operators. K1=AXB, K2=AXB-BXA. Are K1 and K2 hermitian or anti-hermitian?

Homework Statement Hello. I am relatively new to this subject please forgive my incompetence. Please correct me if I have misunderstandings. I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be...

How do I take the cross product of Two 3x3 Matrices. For example what is cross product of: [-1 0 0] [0 1 0] [0 0 1] x [0 -1 0] [1 0 0] [0 0 1] thanks, Della

Can someone explain to me what a dot product and vector product of two vectors are? Be as detailed as possible please! And also why does the right hand rule for vectors work?

A race-car driver is driving in a circle at a fixed velocity. He has a cross hanging down from a string on his rearview mirror. Which of the listed forces impacts the hanging cross as the driver drives around a circle at a fixed velocity? Gravity, Friction, Tension, and Centripetal Force I...

Homework Statement If you make the change of variables: x= ucos(\theta)-vsin(\theta) y= usin(\theta)+vcos(\theta) where the angle 0 \leq \theta <\pi/2 is chosen in order to eliminate the cross product term in: 4x2+8xy+6y2=30 What is the angle you would use? Homework Equations...

I was calculating the cross section for a particular decay and saw that I was off by a factor of half from the known value.. Now, the decay has two identical particles in the final state and I seem to remember having read somewhere that this requires a factor of half...but I am not able to...

I am having difficulty finding the equation or relationship between power (watts) and cross sectional area (m2) to finding the value of an electric field. I am just confused and can't seem to understand and my textbook isn't making sense to me Any help would be appreciated and I...

I'm very confused by this cross product thing...help!

1. Find the sine of the angle between and . 2. AxB = ABsin(alpha) 3. I know T = (3,1,0) and U = (2,4,0), and I calculated that V = TxU = (0,0,10), so the magnitude of V is 10. Then I did 10 = sqrt(10)*sqrt(20)*sin(alpha) Divided 10 by sqrt(10)*sqrt(20), took the inverse...

Cross product and the angles of a prallelogram's diameters Homework Statement With the help of cross product prove: if the angle between the diameters of a parallelogram is 90 degrees, then the parallelogram is a rectangular. Homework Equations A\timesB=(surface of the parallelogram)...

Homework Statement Let \vec{A}, \vec{B}, and \vec{C} be three vectors which are all not in the same plane. Show that \vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\vec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B}) Homework Equations Don't know :( The Attempt at...

I'm studying vector calculus, and have a question about the curl and its relation to a cross product of the del operator and a vector. When doing a standard cross product as the formula I have i(det1) - j(det2) + k(det3), where det1, 2 3 are the appropriate 2x2 determinants. However for the...

The base of a solid is the triangular region bounded by the y-axis and the lines x + 2y = 4, x - 2y =4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse on the xy-plane. So what I did is: 2\int_{x=0}^2...

Hello I am reading this book: "[URL and the appearance of a classical word&f=false"]decoherence[/URL] I hope someone could help me. Please go to Appendix A1 Joos introduces the notation f(q,q'). What is the dimension of f from his notation? Next page he writes that \int f^2 d\Omega...

Could anyone tell me how to use the cross product to prove the sine rule

Why is the cross product defined this way (blah)i + (blah)j + (blah)k = u and used this way (blah)i [SIZE="3"]- (blah)j + (blah)k = u

Where can I get reliable information on the cross section of various substances: boric acid, O2, Uranium, water, etc?

I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX. For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)...

Describe the surface defined by the equation: (a) \vec{r}\cdot \hat{x}= 2, where \vec{r}=x\hat{x}+y\hat{y}+z\hat{z}; (b) \left \| \vec{r} \times \hat{x}\right \|=2 For the first one, I know that is interpreted as the projection of the r vector onto the x-axis is equal to two...

I was reading div grad curl and all that. Couldn't get something basic - cross product. U = iux + k df/dx (ux) V = jvy + k df/dy (vy) UxV = [ -i df/dx - j df/dy + k] uxvy can't figure out how to get U x V.

Homework Statement show that three points P,Q, and R are collinear if and only if vec PQ x vec PR = 0 Homework Equations The Attempt at a Solution i understand this (i can see this visually in my head) but i just don't know how to say it mathematically...i know that the angle...

For the two matrices A and B, (AB)i,j = ri [SIZE="4"]. dj ---- [SIZE="4"]. refers to dot product ---- ri is the ith row in A and dj is the jth column in B. Let us say that A and B are n x n system of column vectors. Then a row vector ri of A would correlate to a component vector of the sum of...