Question

let R^4 have the Euclidean inner product. Find 2 unit vectors that are orthogonal to all three of the vectors u=(2,1,-4,0), v=(-1,-1,2,2)and w =(3,2,5,4) . Guide me, please

Answer 1

@myko

Answer 2

what you tried?

Answer 3

try to find a vector which satisfy the requirement

Answer 4

:)

Answer 5

I would use Gram-Schmidt

Answer 6

common, I tell you I am not allowed to use it now, just after tomorrow class, i will. but not now.

Answer 7

anyway by commun sence, you would like a vector (a,b,c,d) which has no component in u,v,w directions. So use inner product to find it's projection on each of the u,v,w vectors and rest it from this vector

Answer 8

ok, thanks, let me try and tell you the result. if it fix your way by applying Gram. just say yes to mine.

Answer 9

let \[x=\left[\begin{matrix}a\\b\\c\\d\end{matrix}\right]\\
u\cdot x=0,\quad v\cdot x=0\quad w\cdot x=0\quad x\cdot x=1
\]
the four oprthognoality conditions will give you with four simultaneous equations.

Answer 10

i think so, too.

Answer 11

why did I get the medal? heres to myko.

Answer 12

you rather help other than me. but at the end up, you are here. forgive you