c c = ) ([ , , ] ) [ , , ]( [ , , ] a b c c a b c a a b c Example . Prove that ( )) ) ( c a . Treating ( as the first vector on the right hand side of the given equation and using the vector triple product expansion, we get ) ( = (( (( )) c a a c c a . Example .
For any four vectors , a b c d we have ) ( = [ , , ] [ , , ] [ , , ] [ , , ] a b d c a b c d a c d b b c d a . Taking ) as a single vector and using the vector triple product expansion, we get ) ( = Vector Vector Applications of Vector Algebra = ( p d c p c d = (( (( [ , , ] [ , , ] d c c d a b d c a b c d Similarly, taking q , we get ) ( = ( q = ( a q b b q a = [ , , ] [ , , ] a c d b b c d a Example . If , , k b k c , find ( and . State whether they are equal.
By definition, a Then, = ... ( ) = Next, = ... ( ) Therefore, equations ( ) and ( ) lead to ( ≠ . Example .
If , j b k c , verify that (i) ( ) ( [ , , ] [ , , ] a b d c a b c d (ii) (