Orthogonal Definition and 560 Threads

Hello, could someone please give me some help with the following question? Q. Determine all planes (in R³) orthogonal to the vector (1,1,1). This is how I started off but I am not really sure how I need to go about solving this problem. I begin(by somewhat assuming that the vector (1,1,1)...

Hi, this might be very easy, but I forgot how to do the following: I have a vector in R^6: (x1, x2, x3, x4, x5, x6). How do I find a vector such that their dot product vanishes? I know how to do it for the two dimensional case: (x1, x2), so the vector that is perpendicular to it is c(-x2, x1)...

Why a timelike vector and a null vector cannot be orthogonal? Isn't a null vector orthogonal to any vector, by definition? Anyway, each component of a vector is multiplied by zero, so in the end the sum is zero.

Hey there I'm working on questions for a sample review for finals I'm stuck on these three I think I'm starting to confuse all the different theorem, I'm so lost please help 1) Find the coordinate vector of the polynomial p(x)=1+x+x^2 relative to the following basis of P2: p1=1+x...

Find the matrix A of the orthogonal projection onto the line L in R2 that consists of all scalar multiples of the vector [2 5]T . OK...I really don't know how to start off with this problem. If somehow could just help me out there I will try to muddle my way through the rest ! Thanks.

Here is the problem: Determine the orthogonal trajectories of the given family of curves. y = \sqrt{2\ln{|x|}+C} This is what I've done so far: y = (2\ln{|x|}+C)^\frac{-1}{2} y' = -1/2(2\ln{|x|+C)(2/x) Now I understand to find the orthogonal lines I need to divide -1 by...

Let vectorB be a vector from the origin to a point D fixed in space. Let vectorW be a vector from the origin to a variable point Q(x,y,z). Show that vectorW (dot) vectorB = B^2 is the equation of a plane perpendicular to vectorB and passing through D. Thank you for any help

Ok, I'm working with the Pauli Matrices, and I've already gone through showing a few bits of information. I've got a good idea how to keep going, but I'm not exactly sure about this one-- say M= 1/2(alphaI + a*sigma) where alpha E C, a=(ax, ay, az) a complex vector, a*sigma=ax sigmax+ay...

Can anyone give me a physical interpretation of what orthogonal eigenfunctions are please? I understand the mathematical idea, the overlap integral, but I'm not clear about what it implies for the different states. At the moment the way I'm thinking of it is that the energy eigenfunctions of an...

If each spacetime point p_i can be associated with a contant force f_i then the interaction \sum_{i=1}^\infty f_i between points can be described with the use of orthogonal forces.