Question

Let v1=(1,1,0,1), v2=(1,-2,2,1) and v3=(a,a,b,1). For which values and a and b is the set {v1,v2,v3} orthogonal?

Answer 1

vectors are orthogonal if their dot products equal zero.

take the dot product of v1 and v3 and set equal to zero
take the dot product of v2 and v3 and set equal to zero
two equations, two unknowns, solvable.

Check also that v1 and v2 are orthogonal - that is, that their dot prods equal to zero.

Answer 2

Thanks!