If a and b are unit vectors and ( 0 < < ) is the angle between them, then the value of | a + b | | a - b | is equal to...

Step-by-step solution

Given | a | = 1 and | b | = 1 . | a + b |^2 = | a |^2 + | b |^2 + 2 a b = 1 + 1 + 2 = 2(1 + ) = 4 ^2 2 | a - b |^2 = | a |^2 + | b |^2 - 2 a b = 1 + 1 - 2 = 2(1 - ) = 4 ^2 2 Taking the square root, since 0 0 and 2 > 0 : | a + b | = 2 2 | a - b | = 2 2 | a + b | | a - b | = 2 2 2 2 = 2 Answer: 2