# Thread: Determine wether 'u' is orthogonal to span(w)

1. ## Determine wether 'u' is orthogonal to span(w)

Hello,

can someone help me get started on this?

How can i show that u = (-1,1,0,2) is orthogonal to the subspace spanned by the vectors w1=(0,0,0,0) w2=(1,-1,3,0) w3=(4,0,9,2)

how would I set this up..

Thanks!

2. $<\vec{u}~,~\vec{w}_i>=0$

3. That is, a vector $\vec{u}$ is orthogonal to the span of a set of vectors if and only if it is orthogonal to each vector in the set.