Orthogonal sets!

[calculuskid1]

Hey guys, I am brand new to this site, I am originally from the MHF (Math Help Forum), but it seems as if they have shut down Anyways I'm hoping to find a new home here! I'm hoping I'm in the right section here;

So after doing some calculations with the inner product of [a,b,c,d] with X1,X2,X3 I found out that a=b=d and c=-3a. so Y=[a,a,-3a,a] (a cant be 0). So this is orthogonal to all the other vectors, so what am I missing here?
Thanks guys

 

[pka]

So after doing some calculations with the inner product of [a,b,c,d] with X1,X2,X3 I found out that a=b=d and c=-3a. so Y=[a,a,-3a,a] (a cant be 0). So this is orthogonal to all the other vectors, so what am I missing here?

The question does ask for a unit vector.
Thus \(\displaystyle \frac{1}{12}<1,1,-3,1>\) works.

 

[calculuskid1]

Alright, now it says post all unit vectors? As in there is more than one?