Cross product Definition and 471 Threads

Background: we're trying to show that the rate of change of angular momentum of an object about its center of mass (position given by R) is equal to the total torque about R. Why are the terms in red equal to 0? If anything, shouldn't the terms circled in in blue be equal to zero since the...

Homework Statement i am trying to solve for the magnetic torque a circular loop of radius R exerts on a square loop of side length b a distance r away. The circular loop has a normal vector towards the positive z axis, the square loop has a normal towards the +y axis. The current is I in both...

I'm reading a book on microphones and came across the following: and then it goes off talking about something else... I feel stupid for asking this, but I don't get how the above equation works? For one, I thought cross products could only be be involving vectors? Aren't all the terms...

Homework Statement A stiff wire 42.0cm long is bent at a right angle in the middle. One section lies along the z axis and the other is along the line y=2x in the xy plane. A current of 15.0 A flows in the wire-down the z axis and out the line in the xy plane. The wire passes through a uniform...

this is a general question - the thing I'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right this is a vector product question: if i have: (A/c x cB) can i look at that as: (1/c*c)(A x B) which comes to A x B the...

Homework Statement Let A = (-5, -2, -5), B = (-7, -7, -6), C = (-3, -3, 0), and D = (-5, -8, -1). Find the area of the parallelogram determined by these four points. Homework Equations Area of Parallelogram = ||a x b|| The Attempt at a Solution I drew the parallelogram and decided to use CA...

Homework Statement Show that there is no vector ⃗e that has the property of the number 1 for cross product, namely that ⃗e × ⃗x = ⃗x for all ⃗x. Homework Equations I'm sort of stuck on how to show this. The Attempt at a Solution I set e=(e1,e2,e3) and x=(x1,x2,x3) and used cross...

Homework Statement Given |\vec{a}| = 8, |\vec{b}| = 9 and the angle between vector \vec{a} and \vec{b} is 48° find the cross product, \vec{a} X \vec{b}. Homework Equations Let θ = angle between \vec{a} and \vec{b}. \vec{a} . \vec{b} = ( \vec{x}1 * \vec{x}2 ) + ( \vec{y}1 * \vec{y}2 ) + (...

Calculating magnitude and direction of an magnetic force on an electron Homework Statement Okay so the question says that the magnetic force (Vector)FM on a particle which is in a magnetic field is found by (Vector)FM = Vector I x Vector B. Vector I = charge multiplied by the velocity of...

The cross product between two vectors \vec{A}x\vec{B} and \vec{C} is given by the following equation: (\vec{A}x\vec{B})x\vec{C}=(\vec{A}.\vec{C})\vec{B}-(\vec{B}.\vec{C})\vec{A} Well, as I'm sure you know, proving something is true is different than proving how something is true. In this proof...

Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB...

Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB. Homework...

Is it possible to nontrivially represent the cross product of a vector field \vec{f}(x,y,z) with its conjugate as the gradient of some scalar field \phi(x,y,z)? In other words, can the PDE \vec{\nabla}\phi(x,y,z) = \vec{f}(x,y,z)\times\vec{f}^\ast(x,y,z) be nontrivially (no constant...

Here is what I have A=xro+yr1 B=yro+xr1 I need to find A x B I am confused about do it because The components of A and B are in terms of vectors If A = 3i + 4j + 7k and B = 2i + 2j + 1k I would have no problem (these numbers are meaningless just giving an example) finding A...

Explain, for example, why you can cross three vectors (two at a time, following the usual rules), but not dot three vectors. Do you see the dot product "in action" in matrix multiplication? What sort of insights can the dot product give when trying to comprehend matrix multiplication?

I am trying to get an intuition behind the cross product but i seem to get stuck with understanding why we make the vector perpendicular to the other two? I understand the need to define an orientation for physical systems like torque (ccw or cw) but then why make it a vector and why choose...

Homework Statement Find the magnitude of the vector product w ⃗x u, where w=<1,0,1> and u=<1,1,0>. Homework Equations ||w x u|| = ||w|| ||u|| sin θ cos θ = \frac{w.u}{||w|| ||u||} The Attempt at a Solution w ⃗x u ⃗= -i ̂+j ̂+k ̂ ‖||w ⃗x u|| ⃗ ‖= √3 but...

Just learning about vectors in 3 dimensions. Would it be correct to think of the cross product vector like a resultant vector? Is it similar to the displacement? If so, why is it always 90 degrees from both original vectors? If anyone has some deeper insight into any of these vector topics...

Homework Statement For arbitrary vector fields A and B show that; ∇ ^ (A^B) = (∇ . B)A - (∇.A)B + (B.∇)A - (A.∇)B Homework Equations where (A.∇)B = ((A.∇)Bx, (A.∇)By, (A.∇)Bz) and (A.∇)f = Ax δf/δx + Ay δf/δy + Az δf/δz = (Ax, Ay, Az)( δf/δx, δf/δy, δf/δz)f The Attempt at a...

This may be more of a MATLAB question, and if so, I do apologize for posting this in the wrong place. I am doing a project on the Buttke scheme, which is a numerical approximation to the Biot-Savart Law. I am almost finished, but I am having trouble writing the code. The scheme is...

I am trying to figure out the following If R2 = 1.043j -1.143k Then how can R2 = 1.547

Problem: Prove A x (B + C) = A x C + A x B Related equations: Cross product Attempts: Not even remotely sure where to start with this, other than I need to use the cross product rule.

Homework Statement (Z, Q) and (W, S) are two partially ordered sets. There is a relation I on Z x W (Z cross W) that is defined... for all (a, b), (c, d) in Z x W, set (a, b) I (c, d) if and only if aQc and bSd. How does one prove that (Z x W, I) is a partially ordered set? Homework...

I was wondering, is the definition of the cross product the same for complex vectors? And if it is, then how is its geometric interpretation, that is ||\mathbf{a}\times\mathbf{b}||=||\mathbf{a}|| \; ||\mathbf{b}|| \sin\theta Thanks.

Homework Statement Assuming that ∅ is a differentiable scalar valued function and F a differentiable vector field, derive the following identities. a)∇(dotted with)(∅F) = ∇∅(dotted with)F + ∅∇(dotted with)F b)∇(crossed with)(∅F) = ∇∅(crossed with)F + ∅∇(crossed with)F Homework Equations The...

Hi all, Just having some trouble understanding a certain example of cross product. It's actually for physics, but figured it belongs in this forum. In the question I am supposed to cross (dl)y hat with (x1)x hat. So I go (0 dl 0) x (x1 0 0) = (-x1dl)z hat. But turns out the answer the...

I know the cross product and dot product of euclidean space R^3. But I wanted to know if there is a way of thinking the cross product "in terms of" the dot product. That is because the dot product can be generalized to an inner product, and from R^3 to an arbitrary inner vector space (and...

Homework Statement For the general case. I need help finding the cross product for the angular momentum. Say you have a particle at a position r= xi+yj+zk with a velocity of xi+yj+zk and a known mass. How do you find the angular momentum? Homework Equations L=mvr The Attempt at a...

Given the following cross product equation: \vec{A}\times\vec{B}=\vec{C} How to express \vec{A} in term of \vec{B} and \vec{C} (or \vec{B} in term of \vec{A} and \vec{C} ). I think the question I want to ask can also be rephrased as if one was told that a known vector when cross product with...

My question is simple: I understand that if u x v = 0 , then u and v are parallel, but what does that 0 mean? You can't obtain 0 by crossing two vectors. By 0, does it mean (0,0,0)?

F = 5i + 3j Newtons acts 3 m to the right of the origin (x is horizontal and y is vertical). What moment does this force produce about the origin? Use the vector cross product. "Great works are performed

For tangent plane equation z-z0 = f{x}(x0,y0)(x-x0) + f{y}(x0,y0)(y-y0) how come there is no cross product of the partial derivatives f{x} X f{y} to give the normal vector for the plane?

Not sure if this is the correct section. I apologize if it's not. Homework Statement For any vectors \vec{a}, \vec{b}, \vec{c} show that: (\vec{a} \times \vec{b} ) \times \vec{c} lies in the plane of \vec{a} and \vec{b} Homework Equations The Attempt at a Solution I assigned \vec{a} =...

Homework Statement i) Find all vectors v such that <1,2,1> X v = <3,1,-5> ii) Explain why there is no vector v such that <1,2,1> X v = <3,1,5> Homework Equations a X b = <a_{2}b_{3} - a_{3}b_{2}, a_{3}b_{1} - a_{1}b_{3}, a_{1}b_{2} - a_{2}b_{1}) The Attempt at a Solution i) <1,2,1> X v =...

Homework Statement Find a plane perpendicular to the two planes, X+Y=3 and X+2y-z=4 I know i take the cross product of both so i get <1,1,0> and <1,2,-1> But when i do the cross product i get x-y+z book tells me x-y-z what am i doing wrong? Not sure why the z is negative. The...

Homework Statement Not really a homework problem, just a general question. Homework Equations Sorry, I don't yet know how to create arrays/matrices in latex (this is a gif) The Attempt at a Solution In the above image, why is c_{1} positive, c_{2} negative, and c_{3} positive? Aside from...

Use cross product formula in R^4 to obtain a vector that is orthogonal to rows of A Please help with first part and check if i answered the questions correctly. The matrix A = 1 4 -1 2 0 1 0 -1 2 9 -2 2 1. Use cross product formula in R^4 to obtain a vector that is...

Homework Statement Leta theta be the angle between the vectors u=2i +3j -6k and v=2i + 3j+6k A) use the dot product to find cos theta b) use the cross product to find sin theta c) confirm that sin^2(theta) + cos^2(theta)=1The Attempt at a Solution I got a to be 117 degrees, but however b and c...

[b]1. For two differentiable vector functions E and H, prove that (Delta (dot) (e X h) = H (dot) (delta X e) - e (dot) (Delta X h) [b]2. Cross product and dot product. The Attempt at a Solution First I took did the left side of the equation, I took the cross product of vectors e and...

I would like to check my answers... Homework Statement Given nonzero vectors u, v, and w, use dot product and cross product notation to describe the following. A vector orthogonal to u X v and u X w A vector orthogonal to u + v and u - v A vector of length |u| in the direction of v...

Homework Statement Describe all unit vectors orthogonal to both of the given vectors: \vec{a} = 2\vec{i} - 4\vec{j} + 3\vec{k} \vec{b} = -4\vec{i} + 8\vec{j} - 6\vec{k}Homework Equations The cross product of two vectors using the determinant, then dividing by the magnitude of the vector...

Homework Statement show that: ( a - b ) x (a + b ) = 2a x b and wat is its geometric interpretation ?? I'm not sure what's wrong, but i somehow got the value as 2a and not wat was required... PLease help. Homework Equations Since this is a proof, the answer I've arrived at is...

he question asks to find the ratio between E0 and B0 and the ratio between w and k ? E and B are on the x-y plane they are given as verctors without any components dividing no x direction part,y direction part,z direction part so when when i use the maxwell equations \nabla\times...

Can someone please explain to me the motivation for these definitions of the cross product? Let A = (a1, a2, a3), B = (b1, b2, b3). Let A and B be the magnitudes of A and B, respectively, and let \theta be the angle between the vectors. A X B = AB sin(\theta) A X B = (a2b3 - a3b2, a3b1...

Homework Statement It's not a homework question but a doubt I have. Say I want to write \vec A \times \vec B in the basis of the cylindrical coordinates. I already know that the cross product is a determinant involving \hat i, \hat j and \hat k. And that it's worth in my case...

Homework Statement Find the angle between \begin{align*} \vec{A} = 10\hat{y} + 2\hat{z} \\ and \\ \vec{B} = -4\hat{y}+0.5\hat{z} \end{align*} using the cross product. The answer is given to be 161.5 degrees. Homework Equations \left| \vec{A} \times \vec{B} \right| = \left|...

Homework Statement Find a linear transofmration from X={x1,x2,x3} to U={u1,u2,u3} which will remove the cross product term in the quadratic form of equation 2X12+4X22+5X32-4X1X3 and thus write the resulting quadratic form in u1,u2,u3. Homework Equations The Attempt at a Solution No...

Homework Statement \iint \mathbf{F} \cdot \mathbf{dS} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{dA} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{\hat{n}}dA = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \frac{\mathbf{r_u}...

Hi. I've been studying for a test and have been scouring my text for methods of proving points in 3-dimensional space are collinear. The best I can see is that the cross-product of the vectors must equal zero. Can someone explain how to do this a little more clearly?

Hey, I have a problem that can be written in the following form: u=v x w where u, v, w are 3by1 vectors and x is the cross product. now I want to write v in term of u and w, but I have no idea of how to get vector v out of the previous equation. Someone who can help me with this...