Cross product Definition and 471 Threads

Homework Statement if v x w = <5,5,-2> (v cross w) and v * w = 6 (v dot w) then what is the tan(θ) between the two vectors v and w? The Attempt at a Solution well I was thinking v x w = |v||w|sinθ as well as v dot w (v*w) = |v|w|cosθ divide one equation by the other...

Just like the title says, would that technically be true? I know the cross product is normal to the plane of the two vectors being crossed, which would make it z. However, since the angle between two vectors is 0, sin (0) = 0...

Homework Statement Assume that you are given differentiable function f(t) and g(t). Find a formula for the derivative of the cross product u(f(t)) x v(g(t)). Homework Equations d/dt(u(t) x v(t)) = (u'(t) x v(t) + u(t) x v'(t) The Attempt at a Solution So in this case I was thinking...

Homework Statement Calculate the net torque about O at P,assuming that a 30-kg mass is attached at P [Figure 21(B)]. The force Fg due to gravity on a mass m has magnitude 9.8m m/s2 in the downward direction. Homework Equations The torque about the origin O due to a force F act- ing on an...

Homework Statement Calculate the cross product of (3u+4w)xw assuming that uxv=<1,1,0>, uxw=<0,3,1), vxw<2,-1,-1)Homework Equations Possible Relevant eqation: i) wxv=-vxw ii)vxv=0 iii)vxw=0 if and only w= λv for scalar λ or v=0 iV)(λv)xw=vx(λw)=λ(vxw) V) (u+v)xw= uxw+vxw ux(u+w)=uxv+uxw The...

Why does the cross product produce a vector and why is that vector perpendicular to the other vectors? I understand how to calculate a cross product, but why for instance is the cross products of two vectors another vector that is perpendicular to it. Can you prove or explain this to me in...

Homework Statement A=(x,3,1) ,B=(x,-x,2) Determine the value of x if the vector perpendicular to A and B is given by C=(10,-4,-4) Homework Equations The Attempt at a Solution Find A cross B , let A cross B be D . Then D cross C = zero (since they are perpendicular to both A and...

a and b are two vectors and x is the angle between them. ||axb|| = ||a||||b||sinx ------(1) ||axb|| = ||a||||b||||sinx|| ------(2) which one is correct? why?

a =(x,y), b =(h,k) a cross b =? I have idea what to type on google. Is that doing like matrices , a cross b = xk-hy? thanks.

Hi, I was reading vector mechanics by beer and jhonston. I came across the equation wherein the cross prodcut of two vectors P and Q is given. It says P x Q = P x Q` . I am not bale to understand how dis is possible. Because as the vector Q changes even the angle teetha will change then how...

so, the magnitude of the cross product represents the area or volume enclosed by any 2 or 3 vectors respectively, but what does the direction represent? i get that the general direction is one that is perpendicular to all the vectors, but what does the actual direction represent? ie, why the...

How is computed the cross product of complex vectors? Let ##\mathbf{a}## and ##\mathbf{b}## be two vectors, each having complex components. $$\mathbf{a} = a_x \mathbf{\hat{x}} + a_y \mathbf{\hat{y}} + a_z \mathbf{\hat{z}}$$ $$\mathbf{b} = b_x \mathbf{\hat{x}} + b_y \mathbf{\hat{y}} + b_z...

Homework Statement Take P;Q and R three points of R 3 not on the same line. If a = OP , b = OQ and c = OR are the position vectors corresponding to the three points, show that a x b + b x c + c x a is perpendicular to the plane containing P;Q and R The Attempt at a Solution I don't...

Homework Statement If x + v = u Prove x x v = u x v = x x u The Attempt at a Solution I don't even know where to start with this. I thought that magnitude of the resultant vector would have to be equal. So I started messing with each to see if I could find a pattern. x x v = | x||...

One vector with mag 2 pointing East. Other one is mag 4 pointing 30° west of North Would you use sin or cos and would it be - or + I did (2*4)cos60°=+4 because they're vectors and we have the A/H sides. I'm worried about that though because we may use sin? Also Cos is (-) in...

In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?

I am trying to compute -dx i CROSS -x i -y j i,j,k are the unit vectors x is from -∞ to ∞ and y can only be negative. Right hand rule tells me that the cross should be in the negative k direction but computing the cross product gives me y dx k. What's wrong?

Studying outer product spaces at the moment and thought I'd quickly recap on the cross product when I stumbled across this problem which has me fairly stumped! If a,b∈R^3 with a≠0 show that the equation a x u = b has a solution if and only if a.b = 0 and find all the solutions in this case...

I need to prove the identity: \nabla(\vec{A} \times \vec{B})=\vec{B} \bullet(\nabla \times \vec{A}) - \vec{A} \bullet( \nabla \times \vec{B}) I need to prove for an arbitrary coordinate system, meaning I have scaling factors. The proof should be quite straight forward if you use the levi...

Why is the cross product of two vectors perpendicular to the plane the two vectors lie on? I am aware that you can prove this by showing that: (\vec{a}\times\vec{b})\cdot\vec{a} = (\vec{a}\times\vec{b})\cdot\vec{b} = 0 Surely it was not defined as this and worked backwards though. I...

Homework Statement Homework Equations The book says that Torque = the length of the moment arm X the magnitude of the vertical component of F = r X F The Attempt at a Solution My problem is that I don't have any vectors to do a cross product. Instead I tried to...

Homework Statement If a, b, c, d are all vectors contained in the same plane, explain why (a X b) X (c X d) = <0,0,0>Homework Equations The Cross Product! The Attempt at a Solution I know that since all of the vectors are in the same plane that means that a cross product between any of the...

Okay, now that my question has been cleared up, what is the cross product of a constant vector and a vector? Is there a formula?

What is the cross product of a constant and a vector? I know that the cross product between two vectors is the area of the parallelogram those two vectors form. My intuition tells me that since a constant is not a vector, it would only be multiplying with a vector when in a cross product with...

I'm taking multivariate calculus and my teacher just introduced the concept of cross products a week ago. Reading the Wikipedia page, I see that cross products only work in three and seven dimensions, which is puzzling. One use of the cross product for our class is to find the vector...

First question: a x b = -b x a Why is this so? As I understand, a major purpose of the cross product (if not, the purpose) is to find a third vector that is perpendicular to two other vectors simultaneously. Let's say a x b = c. Shouldn't the answer really be, a x b = +/- c? Since, of...

$$ \frac{d}{dt}[\mathbf{a}\cdot (\mathbf{v}\times\mathbf{r})] = \dot{\mathbf{a}}\cdot (\mathbf{v}\times\mathbf{r}). $$ How is this true? Shouldn't the derivative affect the cross product as well?

If e1 and e2 are vectors in ℝ3 show that e1 x e2 = e3, e2 x e3 = e1 and e3 x e1 = e2. I have tried to prove this but I can't get it. My attempt: Step 1: [a1, a2, a3] x [b1, b2, b3] = [a2b3-a3b2, a3b1-a1b3, a1b2-a2b1] Step 2: [b1, b2, b3] x [a2b3-b2a3, a3b1-a1b3, a1b2-a2b1] =...

Homework Statement From John Taylor's Classical Mechanics: Show that definition (1.9) of the cross product is equivalent to the elementary deinition that R x S is perpendicular to both R and S, with magnitude rssinθ and direction given by the right hand rule. [Hint: It is a fact (though...

Homework Statement A 1.47kg particle moves in the xy plane with a velocity of v = (4.59i - 3.28j)m/s. Determine the magnitude of the particle's angular momentum when its position vector is r = (1.35i + 2.57j)m. Homework Equations p = mv L = r x p (the x is supposed to be a cross...

Homework Statement A lever is orientated along the y direction in a Cartesian coordinate system. The length of the lever is 0.5m and one end of it is at the origin of the coordinate system. A (3i-5j)N force applied to the other end of the lever. Calculate the Torque produced by the force...

1. Homework Statement Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j Find A X B (answer only in terms of i, j, k) Find the angle between A and B (answer is terms of degrees) 2. Homework Equations All I was told was that if I set a 3x3 matrix like this: i j k -6 5 0 1 4 0...

Homework Statement Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j Find A X B (answer only in terms of i, j, k) Find the angle between A and B (answer is terms of degrees) Homework Equations All I was told was that if I set a 3x3 matrix like this: i j k -6 5 0 1...

I'm just learning this Latex(sic) formatting, so it's not ideal. I was trying to explore the geometrical significance of the cross product when I happened upon an interesting observation. I've seen things like this before, but never had time to really examine them. I define two vectors...

Hi, I was studying Maths the subject of Vector and found two important rule which are "dot" and "cross" product. I proved the first by myself with the (c^{2}= a^{2}+b^{2}-2.\|a\|.\|b\|.cosθ) However, the I couldn't make out how to prove the other one. I've been so thoughtful about it and need...

Anyone know how would I simplify a cross product where the two vectors have coefficients? For example (x/(y^3))\bar{r} X (x/(y))\bar{L} Thanks!

Homework Statement Calculate the cross product assuming that u X w = <-7,1,8> Find (-3u + 4w) X w = ? Homework Equations I'm not sure. I know you have to relate the cross product to something inorder to find what u and w are, but don't know what equations to use. The Attempt at a...

Examine T= r x F (cross product), where |T|=|r||F| sin t, where t is the angle between r and F The intuitive idea of torque (let's only consider torque about the pivot for now) is that the stronger the force or the further away you are from the pivot point, the more the object will TEND to...

1. See attached image please! 2. For part (a), I applied the cross product and got (-6i - 2k) for (\vec{A}x\vec{B}. I got (6i + 2k) for (\vec{B} x \vec{A}). For part (b), \vec{C} was simply (-6i - 2k) - (6i + 2k) = (-12i -4k). For part (c), the magnitude of \vec{C} was simply 12.65 and for the...

Homework Statement 1. Suppose that u + v + w = 0. Show that u x v = v x w = w x u. What is the geometric interpretation of this result? (Note: The interpretation should explain both the length and the direction). 2. Let v1, v2, and v be three mutually orthogonal vectors in space. Use the...

Homework Statement So I have several problems on my homework which deal with the application of cross product and its magnitude to find areas. I know how to do cross product, and I know how to find the magnitude, however, no matter how many times I try to calculate it, I get the wrong...

I have two problems: Homework Statement In general, what can be said about the vector product x×(x×y) The Attempt at a Solution I thought the result of this would be parallel to y. However the answer suggests it is orthogonal to x. Can anyone explain how I could approach this...

I was doing a question in a test involving the system of moments , you are given 2 force vectors and two points respectively . And you must find a third point and force to make the 3 moments in equilibrium . So I did the cross product with the first force vector and its point and then with the...

Suppose that we have a cross-product of vectors. a × b = c Now suppose that we have an orthogonal matrix M. Is it true that (M a) × (M b) = M c ? My intuition is that here we are moving to another coordinate system and performing a cross product in this new system. I can't find an...

Basically, we have to prove that A X B is equal to ABsinθ Now a crucial step towards the proof is proving that (AXB).(AXB) is equal to (AB)2 - (A.B)2 After that it is fairly simple. But unfortunately, I can not prove the identity. I've tried expanding it into components but things are...

Homework Statement A dot B=0.707m^2, A cross B=4.950m^2 k^. If |A|=2.500m and B makes an angle of 135° with the positive x-axis, what are A and B in component form? Homework Equations A*B = |A||B|cos(θ) A X B = |A||B|sin(θ)@RHR The Attempt at a Solution I have no prior physics...

While we calculate cross product of two vectors let A and B we write ABsinθ. And while we calculate dot product of them we write ABcosθ. Why particularly we use sinθ for cross product and cosθ for dot product.Is there any physical reason why we choose sine for cross product and cosine for...

Why is dot product given by a*b cosθ whereas cross product ab sinθ.

Homework Statement Show that (u+v) x (u-v) = 2v x u Homework Equations being u=(x1,y1,z1) and v= u=(x2,y2,z2)The Attempt at a Solution I've got 2v x u equals: (2y2.z1 - 2z2.y1) + (2x2.z1 - 2z2.x1) + (2x2.y1 - 2y2.x1) But I'm nearly to melt my mind to prove (u+v) x (u-v) = above

Homework Statement Suppose v is a vector satisfying: \alpha v + ( a \times v ) = b For \alpha a scalar and a, b fixed vectors. Use dot and cross product operations to solve the above for v. Homework Equations The unique solutions should be: v=\frac{\alpha^{2}b- \alpha (b \times a) + (b...