- #1
JasonHathaway
- 115
- 0
Homework Statement
Proof that (A×B) . (B×A) + (A . B)^2= A^2 . B^2
Homework Equations
A×(B×C)=(A . C)B - (A . B)C
The Attempt at a Solution
Assuming K=(A×B)
K . (B×A) + (A . B)^2 = A^2 . B^2
B . (A×K) + (A . B)^2 = A^2 . B^2
B . [A×(A×B)] + (A . B)^2 = A^2 . B^2
B . [(A . B)A - (A . A)B] + (A . B)(A . B) = A^2 . B^2
(A . B)(B . A) - (A . A)(B . B) + (A . B)(A . B) = A^2 . B^2