Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

find orthogonal vectors

Status
Not open for further replies.
P

Pulkit Varshney

Member level 5
Joined
Aug 30, 2011
Messages
82
Helped
13
Reputation
26
Reaction score
12
Trophy points
1,288
Activity points
1,731
i have only one vector [x1 x2 x3]. it is 3 dimensional vector.
how can i find its other two orthogonal vectors in which all components must be non zero ?
 

You can use the Gram-Schmidt method:

https://en.wikipedia.org/wiki/Gram–Schmidt_process

Basically, select any 2 random vectors and apply the Gram-Schmidt process to get a set of 3 orthogonal vectors. There is probably an easier method, but that one is straightforward from what I can think of off the top of my head.

In truth there are infinite vectors that are orthogonal to that vector. These vectors lie in a plane, and any two orthogonal vectors in that plane will suffice.
 

Two vectors are orthogonal one each other if their dot product is zero, then I think you just have to find a vector (y1, y2, y3) so that:

x1*y1+x2*y2+x3*y3=0

As said by Shug, in the space there are infinite vector orthogonal to a given one.

If you don't have other costraints I think you can arbitrary assign a value to two variables among y1, y2 and y3 and find the third.
 

actually i am seeking for vectors which are mutually orthogonal, so in 3-d space there can be only 3 such vectors.
and i can not use gram-schmidt here because for that i have to have 3 (non-orthogonal) vectors, but i have only one.
 

Pulkit Varshney said:
actually i am seeking for vectors which are mutually orthogonal, so in 3-d space there can be only 3 such vectors.
and i can not use gram-schmidt here because for that i have to have 3 (non-orthogonal) vectors, but i have only one.
Click to expand...

This is not correct... any two orthogonal vectors in the plane that is orthogonal to the vector will suffice. And you can use Gram-Schmidt; just pick any two random vectors and apply the Gram-Schmidt process to get 3 mutually orthogonal vectors.
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top