Definition: Consider the three vectors 
, 
and 
. If the product of three vectors is a
vector then the multiplication is called vector triple product.
It is denoted by ( × ) × (or) × ( × ) and is defined as
CONCEPTUAL THEOREM
1. Prove that ( × ) × = ( . ) - ( . )
Proof: Let = a1i
= b1i + b2 j
= c1i + c2 j + c3k
( × ) × = i (0 - a1b2c2) - j (0 - a1b2c1) + k (0 - 0)
( × ) × = -a1b2c2 i + a1b2c1 j → (1)
. = c1a1
( . ) = c1a1(b1i + b2j)
( . ) = c1a1b1 i + c1a1b2 j → (2)
. = c1b1 + c2b2
( . ) = (c1b1 + c2b2) a1i
(. ) = c1b1a1 i + c2b2a1 i →(3) (2) - (3)
