Cross product Definition and 465 Threads

Homework Statement If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)? Homework Equations Know how to do the cross product and dot product The Attempt at a Solution For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an...

[SOLVED] derivative of a cross product Homework Statement In some lecture notes I'm reading they jump straight from \frac{d}{d\mathbf{r}}( \frac{m}{2} |\mathbf{\omega}\times\mathbf{r}|^2) to \mathbf{r}\omega^2-\mathbf{\omega}(\mathbf{\omega}.\mathbf{r}) Homework Equations The...

[SOLVED] normalizing a cross product Homework Statement How does normalizing (T(t) x T'(t)) equal ||T'(t)||? Homework Equations r'(t) x r''(t) = ||r'(t)||^2·(T(t) x T'(t)) ||r'(t) x r''(t)|| = ||r'(t)||^2·||T'(t)|| The Attempt at a Solution This doesn't bode well with me...

Homework Statement We know that T(t) = r'(t)/||r'(t)||, or equivalently, r'(t) = ||r'(t)||·T(t). Differentiate this equation to find r''(t), then show that r'(t) x r''(t) = ||r'(t)||^2 · (T(t) x T'(t)). Homework Equations r''(t) = ||r'(t)||'·T(t) + T'(t)·||r'(t)|| The Attempt at...

Is there such a thing as a cross product for R4 vectors? Can you use the permutation symbol to express it in the same way that it can be expressed in R3? Would the correct way to write it be: e _{i,j,k,l} u _{j} v _{k}?

Homework Statement A force F = (5 i - 1 j) N acts on a particle that undergoes a displacement r = (2 i + j) m. (a) Find the work done by the force on the particle. (Calculate all numerical answers to three significant figures.) (b) What is the angle between F and r? * the problem required us...

Homework Statement A, B, C and D are sets if A x B is a subset of C x D then A is a subset of C and B is a subset of D. The Attempt at a Solution My attempt by contraposition. Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A...

Homework Statement Sketch a 3-dimensional picture showing the horizontal plane, a point P on the plane, a vertical line through P, and three vectors at P: vector A points vertically upward; vector B points toward the east; vector C points toward the south. Now determine the cross...

Homework Statement find B from F=q(v X B), where F is magnetic force, q = charge, v = velocity, B = magnetic field. Carrying out 3 experiments, we find that if v_1 = i, (F/q)_1 = 2k - 4j v_2 = j, (F/q)_2 = 4i - k v_3 = k, (F/q)_3 = j - 2i where i,j,k are the unit cartesian vectors This...

Homework Statement Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.) (a) What is AxB when B = 8i + 16j? (b) What is AxB when B = -8i - 16j? Homework Equations AxB=(Axi + Ayj) x (Bxi +Byj) =(AxBx)(i x i)...

I'm having trouble relating the cross product form |a||b|sin(theta) to its component form (a1b2 - a2b1) ... and so on... I know how to do this mathematically so please don't just suggest some proof that I can find in every textbook... The component form involves the solutions to equations...

Homework Statement Show that AXB is not equal to BXA No variables given..just this equation Homework Equations The Attempt at a Solution I don´t know how to start...the only thing I know so far is that AXB is equal to -BXA

Homework Statement I hope I am not posting this question at the wrong place, but can someone explain to me the vector product rule, or cross product rule. I don't seem to get the hang of it. Why I am asking this is because I want to know how force on a moving charge due to an applied...

Homework Statement In Calculus on Manifold pp.83-84, Spivak writes that "if v_1,...,v_{n-1} are vectors in R^n and f:R^n-->R is defined by f(w)=det(v_1,...,v_{n-1},w), then f is an alternating 1-tensor on R^n; therefore there is a unique z in R^n such that <w,z>=f(w) (and this z is denoted v_1...

Homework Statement Given the two vectors written in component-unit vector form below: D = 3\hat{i} - \hat{j} E = 2\hat{i} + 4\hat{j} a.) Find the unit vector in the same direction as D b.) Find the cross product of D x E c.) Write the vector D in magnitude direction form Homework...

Hi all, I have a qustion. dB/ds= -TN, dU/ds= KN (1) N= U x B (2) dN/ds=TB-KU (3) How Eq.(3) can be obtained from Eq.(1),(2)? Have a nice day!

Homework Statement A centripetal-acceleration addict rides in uniform circular motion with period T = 3.22 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2) i + (-9.00 m/s2) j. At that instant, what are the following values? (b) r X a The Attempt at a...

Why is it possible to take the cross product in only 3 and 7 dimensions?

Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...

I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...

How are the exterior products and the cross products related? Wikipedia says: "The cross product can be interpreted as the wedge product in three dimensions after using Hodge duality to identify 2-vectors with vectors."

ok, i don't know what to do with something like this: (d^2R/dt^2 ) + (dR/dt) x B = 0 where the capitals are vectors (sorry i suck at latex). R is a position vector in x-y plane and B is in the z-direction. do i split this into equations for x and y directions separately and solve them...

Hi guyz, I have a small question, In spherical coordinates if we define 2 vectors such as magnetization of a shell M(r,phi,theta) and the magnetic field H(r,phi,theta) As we know the cross product between them is written in the determinant: (Capital means unit vectors) det[(R,r...

hi all. my homework question is what is the derivative of: [(a + t * b) x (a + t * b + t^(2) * c)] a, b, and c are vectors, and t is a constant. * is multipy, ^(2) is squared, and x is cross product. i've been working on it for hours and i have no idea what to do. there's another similar...

While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...

I didn't use the template, because I am not having difficulties with a problem. I am just starting to study rotational motion and there it appears the cross-product. I don't like to memorize formulae that I don't understand it's meaning. Why is \vec a \times \vec b} defined mathematically...

A particle position is described by position vector r = 3i + 2j and the force vector i - 2j acts on the object. 1) Find the torque about an axis through the origin and perpendicular to the xy plane. Draw the two vectors to check your torque direction. I used the right hand rule and found...

In R^3 it is easy to compute the cross product, and i know how to compute it in higher dimensions using wedge product and the hodge star, which shows that it only exists in 3n dimensions. My question is given two vectors in C^3 (complex), is there a neat way to find one perperdicular to...

I am supposed to solve this explicitly for x: x=(x x A)+B where all variables represent vectors. I moved the B vector to the other side and I was thinking i can take a cross product of something with each side to isolate x but do not know what works here, i tried crossing both sides with...

Hello, my problem is as follows: Given that A and B are known vectors, and A \cdot C=u is a known quantity, and A \times C=B Express C in terms of A,B, u, and the magnitude of A So far what i have done was use the definition of the dot product as AC cos \theta=u, and cross product as AC...

This is the question: Two vectors A and B have magnitude A = 3 and B = 3. Their vector product is A X B = -5k+2i. What is the angle Between A and B. OK so I'll start with what I do know. I do know that the cross product is the magnitude of A times magnitude of B times sin theta of B. I end...

Hello, just a quick question. I have two complex numbers (say z and z'), and I want to find the area of the parallelogram that is generated by the two complex numbers (written as vectors, ie, if z = x + iy is a complex number, then the vector is (x,y)). Now the area of the parallelogram...

Hi, my question is the following: \frac{\delta\vec E}{\delta t}\times \vec B = ? In other words, how can i develop this cross product. Are there any identity that reduces this product? Thanks.

Hi guys, I was wondering how I could type a function into MATLAB to computer the cross product of variables. For example I want to compute the cross product of the following: Thanks in advance.

heres the problem. im supposed to use geometric definition to find. (i+J)cross(i-j) I know: v x w=IIvIIIIwIISin[theta] and that The answer comes out to be -2k But what i don't get is looking at the solution manual they show [theta]=pi/4 which i have know clue where that comes from. I was...

Three forces with magnitudes F_a, F_b, F_c act on a point mass, pulling in unit directions a, b, c, respectively. Thr forces are in 'equilibrium' which means that F_aa + F_bb + F_cc = 0 By taking the cross product with a, show that F_b(a \times b) = F_c(c \times a) and find two similar...

hi, I'm currently doing a mechanics module at Uni. The thing is, I'm not very sure about rules regarding the vector cross product and dot product. For example, it says in my notes for angular momentum: "Introducing polar coordinates \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi...

I have learned just about the right hand rule in vector cross product. How is this proved? Can anybody give an example where the cross product plays an important role and where the vector cross product formula is obeyed? Our professor just told us that the torque due to a force acting on a body...

Hey, I have the following question, Simplify (au + bv) x (cu + dv) where a,b,c,d are scalars and u,v are vectors. I know that we can take ab ab and cd outside to make the expression ab(u +v) x cd(u + v) but I am unsure on where to go from here. Thanks in advance

Hello everyone, this should be a simple problem..its for matrices and I already delt with this in calc III and physics but it says: find a unit vector with positive first coordinate orthogonal to both a and b. a = <1,2,1> b = < 1,8,1> so i took the cross product and got: <-6,0,6> it...

I have two vectors A = 2x + 3y - 4z and B = -6x - 4y + z. The problem asks me to find the component of A X B along the direction of C = x - y + z. So I did put A and B into a matrix, but I didn't get the correct answer, which is -14.4. What am I doing wrong?

Hello everyone, I'm stuck on trying to prove the cross product rule for derivatives. I Have to add the right terms and its suppose to be easy but that's what i can't figure out! any help would be great! here is what I have: http://img135.imageshack.us/img135/5540/opopo3ej.jpg

Does anyone know where I can find the derivation of the cross product. I know how to use it and the like but I do not understand why the norm of the matrix : \left[ \begin{array}{ccc}i & j & k \\n1 & n2 & n3 \\m1 & m2 & m3 \\\end{array}\right] yields the vector perpendicular to 'n' and 'm'.

11. Calculate the area of the parallelogram having the vertices (1,2,3),(4,-2,1),(-3,1,0), and (0,-3,-2). To solve this problem I need to find two vectors that share a common point? Then I can take the magnitude of the cross product of those two vectors to find the area of the...

I am having trouble setting this problem up. The problem says: Find a vector N that is perpendicular to the plane determined by the points P(0,1,0), Q(-1,1,2), R(2,1,-1), and find the area of triangle PQR. I know that the cross product of two vectors is perpendicular to the plane of a and b...

Hey guys, Can you help me out with this one. I want to prove the that the cross product |A||B| sin( \theta) is equal to its components, =<a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1> . A thing I find Annoying is that most books just say, we define the dot product in component form as ""...

i need help with the following: note that the big dots represents the dot product 1. suppose that a \bullet b = c \bullet b for all vectors \overrightarrow{b} . show that \overrightarrow{a} = \overrightarrow{c} . i suppose i can't simply divide out the b, right? anyway, i tried...

a crate is sliding (disregard friction) with d=(-3.0 m)i while a steady wind pushes against the crate F=(2.0 N)i + (-6.0 N)j How much work is done by the wind on the crate? Ok W=Fd so I want to multiply the two vectors together. [(-3.0 N)i ]*[(2.0 N)i + (-6.0 N)j ] Do I use a cross...

Why does torque, magnetic fields and others, work with something like the vectorial cross product? A plane director vector of intensity equal to the area of the paralelogram formed by the other two? Anyone? Basic Statistics Physics? Thank you all in advance.

When using cartesian coordinates, I use the following expressions to calculate the cross product of the basis vectors: i \times j = k j \times k = i k \times i = j j \times i = -k k \times j = -i i \times k = -j Can I do the same in polar coordinates? How could I write the cross...