Cross product Definition and 465 Threads

Simple question: is the cross product defined in R^n ? In my linear algebra textbook, they talk about the dot product in length but don't even mention the cross product.

How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?

find the cross product a x b of the vectors a = 5.0m,i and b=4.3m,k 5.0m\ast 4.3m\ast \sin (90)=22m^2,\hat {j} The back of the book gives -(22m^2)\hat {j} Where does the minus sign come from?

I'm not even sure such a thing exists :P. Anyway, if it does, is it correct that it is: Xc = -Y Yc = X (rotation 90 deg counter clockwise) Couldn't find anything about it on google...

I do not understand something about cross products. Say, \vec A\times \vec B=\vec C=(C_x, C_y, C_z) and, \vec C=(A_x \hat x+A_y \hat y+A_z \hat z)\times (B_x \hat x+B_y \hat y+B_z \hat z) but why is this equivalent to (A_x B_y - A_y B_x)\hat x \times \hat y + (A_x B_z - A_z...

Although, the dot product works in infitine dimensions, it is not the case for the cross product. Anybody know in what dimensions the cross product can be defined?

Is there any neat way/rule to write: \vec B \times (\vec \nabla \times \vec A) ? I've tried it myself and found (e.g) for the x-component: \left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_y}{\partial x}+B_z\frac{\partial A_z}{\partial x}\right)-\left(B_x\frac{\partial...

In the problem: A horizontal boom supporting the sign is of uniform construction and weighs 50 N. If the sign weighs 150 N, the tension in the supporting cable is? Could I use the cross product and if so how? The answer is 350 N.

Force F = (4.0 N) i + (-2.0 N) k acts on a pebble with position vector r = (2.50 m) j + (-1.3 m) k, relative to the origin What is the resulting torque acting on the pebble about a point with coordinates (2.0 m, 3.0 m, 2.0 m)? Ok so I just completely forgot how to work with vectors when...

anyone have a clear definition of how to do a cross product?

Find two vectors which are perpendicular, and one of them is twice the magnitude of the other. Also their sum should be (6,8). First of all let the coords be (x,y) and (a,b) then the magnitude of one of them is twice the other i .e . 2 \sqrt{x^2+y^2} = \sqrt{a^2+b^2} also their dot...

Determine whether the points A = (1, 2, 3), B = (1, 1, 1), C = (1, 0, 2), and D = (2,-2, 0) are coplanar and find the volume of the tetrahedron with vertices ABCD. My professor did this problem in class as a review for an upcoming test and he didn't get the answer that was on the key. He...

Okay, here's the question: For r=xi + yj +zk evaluate grad x (k x r), where k is a constant vector. I know how to do the cross product of k x r and I know how to do grad x (k x r). But I don't know what k is. What's k?

Why does the cross product of two vectors produce a vector which is perpendicularto the plane in which the original two lie?(whenever i go to look it up it is already assumed that it is perpendicular)

[SOLVED] dot and cross product vector Hi! The quantity (absolute value vectorA x vectorB close absolute value)^2 + (absolute value vectorA * vectorB close absolute value)^2 is equivalent to: I am confused, a close example used numbers in place of the vectors so I gave it a try in a book I...