If a and b are unit vectors perpendicular to each other, then [ a + ( a b ) b + ( a b ) ( a b ) ] =

Step-by-step solution

Let c = a b . The given scalar triple product is [ a + c b + c c ] . Using the properties of the scalar triple product: [ a + c b + c c ] = ( a + c ) (( b + c ) c ) = ( a + c ) ( b c + c c ) Since c c = 0 , we get: = ( a + c ) ( b c ) = a ( b c ) + c ( b c ) Since the scalar triple product with two identical vectors is zero, c ( b c ) = 0 . = a ( b c ) = [ a b c ] Substituting c = a b back into the expression: [ a b a b ] = ( a b ) ( a b ) = | a b |^2 Since a and b are unit vectors perpendicular to each other, | a