If | a b |^2+| a b |^2=144 ~ &~| a |=4 then | b |=

Step-by-step solution

Using the Lagrange identity for vectors, we have | a b |^2 + | a b |^2 = | a |^2 | b |^2 . Given that | a b |^2 + | a b |^2 = 144 , we substitute this into the identity: | a |^2 | b |^2 = 144 . Given | a | = 4 , we have | a |^2 = 16 . Substituting the value of | a |^2 into the equation: 16 | b |^2 = 144 . | b |^2 = 144 16 = 9 . Taking the square root of both sides, we get | b | = 3 . Answer: 3