If a → and b → are two vectors such that | a → | = 2 , | b → | = 3 and a → + t b → and a → - t b → are perpendicular, where ' t ' is a positive scalar, then

Step-by-step solution

We know that, Dot product of perpendicular vectors is zero. ∴ a → + t b → · a → - t b → = 0 ⇒ a → 2 - t a → · b → + t b → · a - t 2 b → 2 = 0 ⇒ a → 2 - t 2 b → 2 = 0 ⇒ 4 - 9 t 2 = 0 ⇒ t 2 = 4 9 ⇒ t = ± 2 3 But given that t is positive scalar, hence t = 2 3 .