If | a | = 4, | b | = 3 and a b = 8 then [ a a + b a b ] =

Step-by-step solution

Using the properties of the scalar triple product: [ a a + b a b ] = [ a a a b ] + [ a b a b ] Since the scalar triple product is zero when two vectors are identical, [ a a a b ] = 0 . [ a a + b a b ] = [ a b a b ] This can be written as: [ a b a b ] = ( a b ) ( a b ) = | a b |^2 Using Lagrange's identity: | a b |^2 = | a |^2 | b |^2 - ( a b )^2 Substituting the given values | a | = 4 , | b | = 3 , and a b = 8 : | a b |^2 = (4)^2 (3)^2 - (8)^2 | a b |^2 = 16 9 - 64 | a b |^2 = 144 - 64 = 80 Answer: 80