How to get ortognol vectors from a vector?

[bee]

can anyone plz tell me how to caluculate the orthognoal vectors like U2 and U3 from vector U1 such that these three are orthognol to each other?


Waiting....

 

[mkhan]

One method to get orthogonal vectors and then orthonormal vectors from a vector is to use Gram-schmidt process. For complete process of Gram-Schmidt see "Linear Algebra and Its Applications" by Gilbert Strang.

Arif Khan

 

[safwatonline]

let U1=a i+b j + c k
where a , b , c are known
to get a vector U2 orthognal to it
then let U2=x i+ y j+z k
where (x+a)+(y+b)+(c+z)=0
this is one equation in three variable whch means infinite solutions which is true

 

[Slayerza]

Also to check your work the 3 vercors U1, U2, U3 must be orthogonal to each other, thus the inner product of the vectros must be 0

<u1,u2> = <u1,u3> = <u2,u3> = 0

If the above holds (which it should if your algebra is correct) you will have 3 vectors ortogonal to each other.

Cheers
Slayer

 

[mmatica]

The simplest method is to start with any vector V which is not collinear with U1 and define (using the vector product "x"):

U2 = U1 x V
U3 = U1 x U2

Mate