For any vector a → = a 1 i ^ + a 2 j ^ + a 3 k ^ , with 10 a i < 1 , i = 1 , 2 , 3 , consider the following statements: A : max a 1 , a 2 , a 3 ≤ a → B : | a → | ≤ 3 max a 1 , a 2 , a 3

Step-by-step solution

Given, a → = a 1 i ^ + a 2 j ^ + a 3 k ^ , with 10 a i < 1 , i = 1 , 2 , 3 , Let us assume that a 1 ≤ a 2 ≤ a 3 Now we know that, a → 2 = a → 1 2 + a → 2 2 + a → 3 2 And a → 3 2 ≤ a → 1 2 + a → 2 2 + a → 3 2 So, combining both above equations we get, ⇒ a → 2 ≥ a → 3 2 ⇒ a → ≥ a → 3 = max a → 1 , a → 2 a → 3 Hence, A is true Now again solving, a → 2 = a → 1 2 + a &