Quadratic Programming Setting up Constraint

I am trying to set up a simple OLS model with constraints on the coefficients in R. The code below is working. However, this demonstrates

y = c + a1x1 + a2x2 + a3x3 with constraint a1+a2 = 1

I would like to revise this constraint to: a1*a2 - a3 = 0

thanks for your help!

WORKING CODE:

'''

    set.seed(1000) 
    n <- 20
    x1 <- seq(100,length.out=n)+rnorm(n,0,2)
    x2 <- seq(50,length.out=n)+rnorm(n,0,2)
    x3 <- seq(10,length.out=n)+rnorm(n,0,2)
    constant <- 100
    ymat <- constant + .5*x1 + .5*x2 + .75*x3 + rnorm(n,0,4)
    xmat <- cbind(x1,x2,x3)

    X <- cbind(rep(1,n),xmat) # explicitly include vector for constant
    bh <- solve(t(X)%*%X)%*%t(X)%*%ymat

    XX <- solve(t(X)%*%X)
    cmat <- matrix(1,1,1) 
    Q <- matrix(c(0,1,1,0),ncol(X),1) # a1+a2=1 for y = c + a1x1 + a2x2 + a3x3
    bc <- bh-XX%*%Q%*%solve(t(Q)%*%XX%*%Q)%*%(t(Q)%*%bh-cmat)

   library(quadprog)
   d <- t(ymat) %*% X
   Rinv = solve(chol(t(X)%*%X)) 
   qp <- solve.QP(Dmat=Rinv, dvec=d, Amat=Q, bvec=cmat, meq=1, factorized=TRUE)
   qp

   cbind(bh,qp$unconstrained.solution)
   cbind(bc,qp$solution)

'''