Cross product Definition and 465 Threads

Homework Statement Let P be a point not on the plane that passes through the points Q, R and S. show that the distance d from P to the plane is d = (|a.(bxc)|)/(|axb|) where a = QR and b = QS and c = QP (those are lines between given two points) Homework Equations |axb| =...

This might be math problem, but I only see it in EM books. \nabla X (\vec A X \vec B) \;=\; (\vec B \cdot \nabla)\vec A - \vec B(\nabla \cdot \vec A) -(\vec A \cdot \nabla)\vec B + \vec A ( \nabla \cdot \vec B) . What is \vec A \cdot \nabla ?

Homework Statement Hi there. I am currently taking physics 30(algebra physics course) and we are in the electrostatics unit. I am curious as to why, when trying to find the force acting on a charged particle moving perpendicular to a magnetic field, the force results in a direction that is...

in a many particle system we have a center of mass R and position vector of the ith particle with respect to centre of mass is r_i. hence the position vector measured from the origin is R_i=R+r_i. why does R\times\sum (m_i \dot{r}_i) =0, where \dot{r}_i denotes the rate of change wrt time...

Homework Statement Two vectors A and B have magnitude A = 2.99 and B = 3.10. Their vector product is A X B = -4.98 k + 2.08 i . What is the angle between A and B? Homework Equations C= ABsinθ C=A X B The Attempt at a Solution θ= arcsin C/(⎮A⎮⎮B⎮) so i found the magnitude...

I have a number of books which give a vector identity equation for the curl of a cross product thus: \nabla \times \left(a \times b \right) = a \left( \nabla \cdot b \right) + \left( b \cdot \nabla \right) a - b \left( \nabla \cdot a \right) - \left( a \cdot \nabla \right) b But doesn't b...

Does anyone knows how to compute cross product vector of more than 3 dimensions? It seems all the linear algebra textbooks only discuss 3D cross product vector. What are the formulas?

I've been trying to find what the square of two cross products is and can't find it. Can anyone tell me the identity for (A X B)^2 ?

Assume that X^1,X^2,\ldots, X^k are vectors in \mathbb{R}^n, and 1\leq k\leq n. Is there a simple formula for the k-dimensional measure of the generalised "quadrangle" spanned by these vectors? If k=n, then the solution is |\textrm{det}(X)| with X_{ij}=(X^{j})_i. If k=2 and n=3, then the...

cross product question.. "find the magnitude of the force" Homework Statement A wrench 0.9 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of <0, 3, -2> at the end of the wrench. Find the magnitude of the force in Newtons...

Homework Statement If the cross product of vector v cross vector w = 3i + j + 4k, and the dot product of vector v dot vector w = 4, and theta is the angle between vector v and vector w, find tan(theta) and theta. Homework Equations vector c = |v||w| sin(theta) where vector c is the...

Homework Statement I have 2 (3d)vectors A and B and I want to find a vector C perpendicular to both of them. A = 3i-2j+4k B = -2i+5j-2k C = Cx+Cy+Cz Homework Equations So we know A dot C = 3Cx-2Cy+4Cz and B dot C = -2Cx+5Cy-2Cz The Attempt at a Solution

Homework Statement Find the distance from the point (2, 4, 4) to the line x = 0, y = 4 + 3t, z = 4 + 2t. Homework Equations The cross product and the dot product and d = |n * b|/|n| The Attempt at a Solution So the distance from the point to the line is the line directly...

Homework Statement hi i was wondering how exactly one should find the distance of a point to a line using cross product for example, the distance from A(1,2,0) to a line running through B(0,1,2) & C(3,1,1) with Y being angle between BA and BC BC = 3,0,-1 BA = 1,1,-2 so by using...

An orientation of a real n dimensional vector space V is an equivalence class of an ordered basis. Equivalently, this corresponds to a choice of a generator of H_n(V,V-0)=Z. The correspondence between the two is this: given an ordered basis (v_1,...,v_n) of V, the convex hull of...

Hi, I've been trying to derive the electromagnetic stress tensor on my own, and I've run into a bit of a problem. I have a cross product of a curl (\vec{E}\times(\nabla\times\vec{E})) that I need to expand, and the typical...

Homework Statement This is a physics problem. need to find torque on dipoles the the 2 dipoles are on the same plane with distance r p1 is pointing up while p2 is pointing right Homework Equations N=PxE The Attempt at a Solution I know how to do a cross product, you make the...

A 5.0 kg object at r= i^+2j^+3k^ meters has an acceleration a=5i^+6j^-7k^ m/s^2 a)what is the objects torque around the origin of the cordinate system b)prove that the torque is perpendicular to the position vector r a) t^=rXma=-10<16,-11,2> t=-10(381)^1/2 b) <1,2,3>*<16,-11,2>=0

Could someone please clarify a simple order of operations related to cross product? A x (B x C) = ? I am not sure between the these two options: = (A X B) x (A X C) or = do stuff in parenthesis first then cross with A

My final for Physics is coming up and I really, really ****ed up in this class. I don't even know how to do dot products, cross products, or let alone Newton's laws. We applied Newton's laws to some pulley problems I think. I've been going to all the lectures but it just doesn't stick -- nothing...

Can I use cyclic rotation in \vec{a} = \vec{b} x \vec{c} and say: \vec{c} = \vec{a} x \vec{b} \vec{b} = \vec{c} x \vec{a} for any vectors \vec{a}, \vec{b} and \vec{c} or only if they are perpendicular to each other? If it's only a special case: is there a way to express \vec{b} and...

Homework Statement cross product of i x -i Homework Equations i x i =0, i x j = k, etc. The Attempt at a Solution I'm guessing it would be zero, just making sure because I keep getting the question I'm working on wrong.

Homework Statement I'm solving a physics problem using cross products and I think I might be doing the cross products wrong Homework Equations I'm using the formula: a cross b = (a2b3- a3b2)x + (a3b1- a1b3)y + (a1b2- a2b1)z where a1 = ax, a2 = ay, a3 = az, etc. I don't know if this...

Hello! I have a quick question regarding the intersection of three planes if the determinant is 0. If there are solutions, there will be an infinite number of solutions. One of the equations for the plane can be ignored as it is a linear combination of the other two, and can be ignored for...

If Fmag = q(v x B) and Felectric = qE, Florentz = q [E + (v x B)] can I say that Florentz = Fmag + Felectric?

Homework Statement A rod has one end at the origin and one end at the point P whose coordinates are (1m, 2m, 2m). A force F = (3i+2j-1k) N acts on the rod at the point P. What is the torque about the origin due to F? Homework Equations torque = F x r The Attempt at a Solution I'm...

cross product "associative triples" Homework Statement We know that the cross product is not associative, i.e., the identity (1) (\vec{a}\times\vec{b})\times\vec{c} = \vec{a}\times(\vec{b}\times\vec{c}) is not true in general. However, certain special triples \vec{a};\vec{b};\vec{c} of...

Homework Statement A= ci-2j+k B=i+2j-k Find c that makes the vector(A-B) perpendicular to the vector B Homework Equations AXB = (AxBy-AyBx)k+(AzBx-AxBz)j+(AyBz-AzBy)i The Attempt at a Solution A-B=(c-1)i-4j+2k I said that since (A-B) is perpendicular to B then |A-B| * |B| =...

Hello. I am taking a fundamentals of electromagnetics. There are couple of formulas I have been using without understanding the concepts. \nabla \cdot B = 0 \nabla X E = 0 (curl free) In those cases, what do dot and cross product mean? Thanks.

Homework Statement Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2. a)What is 5(vector A) dot vector B? b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude...

How do you find the cross product when you are given two vectors in R2? i know how to do it for R3

Homework Statement A vector of magnitude 17 units and another vector of magnitude 7.4 units differ in directions by 27°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product ×. Homework Equations Right-hand rule, a*b=abcos(theta), A x B=...

Homework Statement the question is sample problem 11-3 of 'fundamentals of physics' 7th edition. Three forces, each of magnitude 2.0N, act on a particle. the particle is in the xz plane at point A given bz position vector r, where r0 3.0M and theta=30°. Force f1 is parallel to the x...

Homework Statement vector A = 1.5i + 6.7j - 7.4k vector B= -8.2i + 6.5j + 2.3k (f) What is the magnitude of the component of vector A perpendicular to the direction of vector B but in the plane of vector A and B. The Attempt at a Solution This part of the problem has me kinda...

This problem involves vectors and it's a fairly basic proof but I can't seem to wrap my head around it. I tried to just separate the vectors into their components and cross them but then I just get another set of coordinates that doesn't seem factorable. I really can't see any way to...

Homework Statement This is actually a concept question, but since its kind of elementary i post it here I understand the calculation of the cross product, what i do not understand is why the cross product that only involve in 2 dimension will have the result of 3rd dimension Homework...

... with the cross product being only defined as: A X B = |A| |B| sin \theta times a unit vector perpendicular to the plane of A&B (direction according to the right hand rule, in the usual way). where theta is the smallest angle between vectors A & B. A X ( B + C ) = A X B + A X C is the...

Homework Statement Show graphically how \vec{a}\times\vec{x}=\vec{d} defines a line. \vec{a} and \vec{d} are constants. \vec{x} is a point on the line.Homework Equations \vec{a}\times\vec{x}=a\cdot x\cdot sin(\theta)\cdot \hat{n}The Attempt at a Solution Not sure if the included relevant...

The pure math of the problem: I have two vectors, both of which are expressed in spherical coordinates. I know the magnitudes as well as the polar and azimuthal angles that express these vectors. In addition, I have a third vector. I only know the magnitude of this vector, and I need to...

Would you pls help me with the following vector product? I got no idea how the author derived the second equation from the first one. My derivation result is always including the imaginary unit i for the second term in the second equation on the right hand side. Specifically, how to verify that...

hi, I'm trying to follow a derivation in a paper and this equation is confusing me: (u'.\nabla)U = (\nablaU).u' Where U and u' are velocities. The operation of del on the vector U without a dot or cross product is giving me some grief. Can someone explain how this works to me...

Homework Statement http://damtp.cam.ac.uk/user/dt281/dynamics/two.pdf" Looking at page 5, equations (2.19) and (2.20) The Attempt at a Solution I cannot understand how they derived the (2.20), at first from comparing the solutions I had assumed r(dot)' had disappeared as we were...

Hi there!I'm trying to prove the following obvious statement, but am somehow stuck :( Let \vec a,\ \vec b\in\mathbb{R^3} , let M be in SO(3) and x be the cross productprove: M(\vec a\times\vec b)=M\vec a\times M\vec bI tried using the epsilon tensor, as in physics, but it doesn't really...

i'm reviewing for a test and I can't remember how to do the cross product of (2A)x(3B) or how to find the angle theta when given components. or dot product: 2A . 3B

Homework Statement Prove that If \vec{a}x \vec{b} = 0, then \vec{a}is parallel to \vec{b}. Homework Equations The Attempt at a Solution I tried attempting the solution by using the following: \vec{a} = [a1, a2, a3] \vec{b} = [b1, b2, b3]When I took the cross product of a x b I got...

Hi Guys, I realize that this may seem like a really simple question but it's really driving me crazy. In my A-level maths we've just started looking at the cross product and I understand how to calculate it, it's application in calculating areas ect but I find myself not understanding what...

Did someone just realize that taking the determinant of a specific matrix gives you the cross product formula, or is there is a specific conceptual reason why it works?

I understand the cross product of vectors to some degree and i can calculate. But i don't really understand the origin of the cross product What does a vector cross product mean in physical terms. Vector addition is quite easy to understand. I don't think the cross product is 'multiplication...

Homework Statement Is the line through (4,1,-1) and (2,5,3) parallel to the line through (-3,2,0) and (5,1,4)? Homework Equations The Attempt at a Solution Line one 'direction' = (-2,4,4) = A Line two 'direction' = (8,-1,4) = B I remember that the cross product of two...

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)...