[R] help computing a covariance

[Eugene Salinas (R)]

Hi everyone,

(This is related to my posting on chi-squared from a day ago. I have 
tried simulating this but I am still unable to calculate it analytically.)

Let y be an n times 1 vector of random normal variables mean zero 
variance 1 and x be an n times k vector of random normal variables mean 
zero variance 1. x and y are independent.

Then P is the projection matrix  P=x*inv(x'*x)*x'

I need to figure out the covariance
 
Cov ( y'*P*y , (A'*x'*y)^2 ) where A is a constant of dimension k times 1.

thanks, eugene.