Question 29494
 Don't use a to represent a vector. I use u instead.

 And u^T x means the inner (dot) product of <u, x>

 W={x: u^Tx=0}. Provce that W is a subspace of R^3.

 proof: If x, y in W, a, b in R, then
 u^T (ax+by) = a u^x + b u^y = 0 
 --> W is a subspace.

 (<u, ax+by> = a<u,x> + b<u,y> & 
  <ax+by, u> = a<x,u> + b<y,u> called bilinear)

 You have to work hard.

 Kenny