Cross product Definition and 471 Threads

Hi all, I am very confused on how to define the vector product or cross product in a physical sense. I know the vector product is a psuedovector, and that it is the area of a parallelogram geometrically. However, I know it used used to describe rotation in physics. As with torque, magnetism and...

Homework Statement Find the set of points of M such that: AM x BC=AM x AC (Vectors) The Attempt at a Solution [/b] AM x (BM+MC) =AMx(AM+MC) AMxBM+AMxMC=AMxAM +AM x MC Then AMxBM=0 MA X MB=0 I am new to this lesson and this is my first time i solve such a question and i had no idea...

Mod note: Member warned about posting with no effort. 1. Homework Statement Expand to the general case to explore how the cross product behaves under scalar multiplication k (a x b) = (ka) x b = a x (kb). The Attempt at a Solution would this be the right general case to portray the situation?

If I choose the positive y direction to be vertically downwards, and the positive x direction to be to the right, and take the cross product y cross x, then the direction of the resultant is out of the page (if I draw x and y as lines on paper). The magnitude is yx sin(φ), where φ is the angle...

Homework Statement This is a general question about the equation. So, I know that the cross product requires a vector in at least 3 dimensions crossed with another. Here is the formula that I am using: uxv = My problem is the negative/positive sign orientation in front of the y element and z...

Homework Statement Calculate (A×B)⋅C for the three vectors A with magnitude A = 5.00 and angle θA = 25.1∘ measured in the sense from the +x - axis toward the +y - axis, B with B = 4.18 and θB = 62.0∘, and C with magnitude C = 5.82 and in the +z - direction. Vectors A and B are in the xy-plane...

Homework Statement Given position function r(t) and r'(t) = c X r(t), where c is some constant vector, describe the path of the particle. In other words, describe r(t). Homework Equations // The Attempt at a Solutiona) r'(t) points in the direction of motion. If we can understand how r'(t)...

When we talk about the angle between two vectors while computing the cross product, which angle are we referring to exactly? According to most sources, the angle should be between 0 and π; yet according to my math book, "the angle is measured in an anticlockwise sense from a to b, if the vector...

Hello, I'm having some difficulty with a conceptual question on a practice test I was using to study. I have the answer but not the solution unfortunately. 1. Homework Statement "For every differentiable function f = f(x,y,z) and differentiable 3-dimensional vector field F=F(x,y,z), the...

Homework Statement There is a sphere of magnetic material in a uniform magnetic field \vec H_0=H_0\vec a_z, and after some calculations I got the magnetic moment vector \vec M_0=M_0\vec a_z, where M_0 is something that isn't important to my question. I am unsure if this magnetic moment vector...

Homework Statement I could prove a, trying b now. Homework Equations The definition of the cross prod.? The Attempt at a Solution https://www.dropbox.com/s/0sauaexkl4j2yko/proof_cross_prod.pdf?dl=0 I did not manage to get a scalar times v and a scalar times w. (No need to point this...

Homework Statement Given that \vec{V} and \vec{W} are vector operators, show that \vec{V}\times \vec{W} is also a vector operator. 2. The attempt at a solution The only way I know how to do this is by showing that the commutator with the angular momentum vector operator ( \vec{J}) is zero...

Homework Statement Find vector product of C = A \times B of two vectors in oblique coord. system. Give explicit expressions of components of C in covariant and contravariant components (constructing reciprocal basis from direct basis will be useful). Homework Equations I am basically just...

Homework Statement Considera 1.0 C charge moving with a velocity of v = -2.0i + 2.0j - 1.0k in a magnetic field of B = -4.0i + 1.0j – 3.0k. What force is this charge experiencing? What is the angle between the velocity and magnetic field vectors? Homework Equations F = q(E + v x B)...

Homework Statement Use the LC symbol to calculate the following: $$\nabla \times \frac{\vec{m} \times \hat{r}}{r^2}$$ Where ##\vec{m}## is just a vector, and ##\hat{r}## is the unit radial vector and ##r## is the length of the radial vector. Homework Equations On the Levi Civita symbol...

Is this just a coincidence that cross product can be found from determinant of 3*3 matrix? what is the differences between wedge product and cross product?Thanks.

A fluid motion has velocity $$\underline{u}=\sin{(at)}\hat{\imath}+\hat{\jmath} \times r +\cos{(at)}\hat{k}$$ I need to know what is $$\hat{\jmath} \times r$$ to find Vorticity and other things.

Is there an intuitive reason or proof demonstrating that in general dimensions, there is no direct analogue of the binary cross product that yields specifically a vector? I came across Wedge Product as the only alternative, but am just learning linear algebra and don't quite comprehend yet...

HEY GUYS! (Wave) ok so i have this question i did. and now I am reviewing for the test and i looked at how i did it and i did in the most complicated way ever. i don't FULLY understand chegg's method. so i hope someone can provide me with the SIMPLEST method possible. thank u! (Blush) (p.s...

Homework Statement Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established. I need to find the area using the cross product. Homework...

Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...

Homework Statement Vectors A & B lie in an xy plane. A has a magnitude 7.4 and an angle 142(deg) with respect to the +x direction. B has components (-6.84i, -7.37j) B) What is the angle between the -y axis and the direction of the Cross product between A and B? Homework Equations Cross...

Hi there. I wanted to demonstrate this identity which I found in a book of continuum mechanics: ##curl \left ( \vec u \times \vec v \right )=div \left ( \vec u \otimes \vec v - \vec v \otimes \vec u \right ) ## I've tried by writting both sides on components, but I don't get the same, I'm...

Definition/Summary The cross product of two vectors \mathbf{A} and \mathbf{B} is a third vector (strictly, a pseudovector or axial vector) \mathbf{A}\times\mathbf{B} perpendicular to both of the original vectors, with magnitude equal to the product of their magnitudes times the (positive)...

I understand that dot product of vectors means projecting one vector on to the other. But I don't understand what is the physical significance of a cross product? I have read that cross product gives the area of the parallelogram which has each of the vectors as its sides...but why do we want to...

1. Here is the prompt: http://imgur.com/mfbPidG 2. F = qv x B 3. At first this seemed like a simple cross product problem, and it probably still is, but I'm really confused as to what "3.70E6 m/s/ in the (i+j+k)/sqrt(3) direction" means, so I don't know how to set up my problem anymore. Could...

Here is the claim I am trying to prove: Suppose we have two vectors \mathbf{r} and \mathbf{s}. I would like to show that there are only two directions in which the resultant vector of the cross product \mathbf{r} \times \mathbf{s} can point, parallel and antiparallel. How might one prove...

1."In this exercise, you will be finding the resultant torque from the cross product of a lever arm with a force vector. The lever arm vector is A=2.0i+3.0j. The force vector is B=3.0i-4.0j. Find A x B B x A and 2A x 3B 2.My teacher has been sick the past few days so hasnt taught us...

If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...

Cross product is used to find the perpendicular vector of two vectors. If there is any two vectors in a plane then there is always a perpendicular vector to both of them. So in circular motion if the motion is horizontal then is there a perpendicular force to the object in circular motion?

Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..

I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...

If u × v = u × w, so v = w ?

Hi all, I'm trying to work out how I can get the set at specific index in a cross product without creating the whole product. For instance: I have array A of length 512 I also have a number that specifies how many times that array needs to be 'cross-producted' against itself. This gives me...

I understand that the cross product, in lay mans terms doesn't exist unless we're in 3 dimensions. When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector. So if we are talking about measurable...

Hi everyone, What does \int \vec{f} × \vec{dl} mean? does it mean "The Line Integral of Vector Function on a positive curve L"? And are the following named correctly? \int \vec{f} . dl : Scalar Line Integral of a Vector Function \int udl : Line Integral of a Scalar Function

Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?

I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may...

Homework Statement In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly...

Some background: I am self studying dynamics and I have encountered a fundamental problem with either my understanding of linear algebra, or I am just plain dumb. So, I print screened the page of the book we're on. Now let me try to reduce some ambiguity in my question, I have a general...

I have a nice table that shows the dot product between unit vectos (see annex). I'd like know how is the cross product between unit vectos of all basis. Do you have a table with such information?

I was thinking, if exist a product (cross) between vectors defined as: \vec{a}\times\vec{b}=a\;b\;sin(\theta)\;\hat{c} and a product (dot) such that: \vec{a}\cdot\vec{b}=a\;b\;cos(\theta) Why not define more 2 products that result: \\a\;b\;sin(\theta) \\a\;b\;cos(\theta)\;\hat{d} So, for...

True or False, if AxB = AxC then either A=0 or B=C. A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?

Hi, So I still not sure how to apply like rhr rule in this setup in problem like the one in the following so I tried to do rhr in order to get the direction but it didn't work out. this is an example from halliday and resnick book. Figure 32-24 shows a wire segment,placed in a uniform...

can you show me derive cross product from dot product?

hey all well the title says it all. if i want to take the cross product of two matrices, how do i do it? any help, advice, etc. is very appreciated! thanks

How do you take the cross product of two 4-Vectors? \vec{r} = \left( \begin{array}{ccc}c*t & x & y & z \end{array} \right) \vec{v} = \left( \begin{array}{ccc}c & vx & vy & vz \end{array} \right) \vec{v} \times \vec{r} = ?

okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because this is a bit confusing to describe only with words: for example we have this http://farside.ph.utexas.edu/teaching/301/lectures/img243.png and then if we use the cross product of...

i have a vector xK where k is the unit vector perpendicular to other unit vectors i and j when i multiply a force which has 5k for instance another which has ( 3 i + 4 j ) i multiply 5k by 3i then 5k by 4j right ? the answer would be ( 15 j - 20 i ) right ?

Homework Statement My textbook says: The length of the cross product a x b is equal to the area of the parallelogram determined by a and b. How can a length equal and area? They have different units?