Problem:

Consider the vector

in

Find a basis of the subspace of R^4 consisting of all vectors perpendicular to .

I'm not very sure about how to solve this problem. I assume that I need to find a set of vectors for which the case holds.

I tried using the formula,

Since I already know , I would just need to figure out . To do this, I used projection.

This is where I get stuck, because I'm LOOKING for the u vectors... correct?

Am I far off the path I should be on here or am I on the right track?

Any help is greatly appreciated. Thanks for reading.