Parametrization of $a^2+b^2+c^2=d^2+e^2+f^2$ Is there an existing parametrization of the equation above that is similar to Brahmagupta's identity for $a^2+b^2=c^2+d^2$? I need either a reference to look it up or a hint to solve it. Thanks.

Above equation (a^2+b^2+c^2)=(d^2+e^2+f^2) has parametric solution. 
Refer to Tito piezas on line book "collection of algebraic Identities".
Section sum of squares. The answer is given below;
(a,b,c)=[(p+q),(r+s),(t+u)]  and
(d,e,f)=[(p-q),(r-s),(t-u)]
Condition is (pq+rs+tu)=0
After parametrization of (pq+rs+tu)=0, the parametric solution in 
one variable is given below:
(a,b,c)=[(4k^2+12k+1),(3k-8),(7k+28)]    and
(d,e,f)=[(4k^2+12k-13),(k+2),(13k+26)]

