If A → + B → = a → , A → · a → = 1 and A → × B → = b → , then

B → = b → × a → + a → | a → | 2 - 1 | a → | 2

B → = a → × b → + a → | a → | 2 - 1 | a → | 2

A → = b → × a → + a → | a → | 2

If a → , b → , c → and d → are the unit vectors such that a → × b → · c → × d → = 1 and a → · c → = 1 2 , then

a → , b → , c → are non-coplanar

a → , b → , d → are non-coplanar

a → , d → are parallel and b → , c → are parallel

If a → and b → are vectors in space given by a → = i ^ - 2 j ^ 5 and b → = 2 i ^ + j ^ + 3 k ^ 14 , then the value of 2 a → + b → · a → × b → × a → - 2 b → is

Given, a → = i ⏜ - 2 j ⏜ 5 and b → = 2 i ⏜ + j ⏜ + 3 k ⏜ 14 . Here, a → = b → = 1 And a → · b → = i ⏜ - 2 j ⏜ 5 · 2 i ⏜ + j ⏜ + 3 k ⏜ 14 ⇒ a → · b → = 2 - 2 5 14 = 0 Now, 2 a → + b → · a → × b → × a → - 2 b → ⇒ 2 a → + b → · - a → - 2 b → × a → × b → ⇒ - 2 a → - b → · a → - 2 b → × a → × b → ⇒ - 2 a → - b → · a → × a → × b → - 2 b → × a → × b → ⇒ - 2 a → - b → · a → × a → × b → - 2 b → × a → × b → ⇒ - 2 a → - b → · a → · b → a → - a → · a → b → - 2 b → · b → a → - b → · a → b → ⇒ - 2 a → - b → · a → · b → a → - a → 2 b → - 2 b → 2 a → + 2 b → · a → b → ⇒ - 2 a → - b → · 0 - b → - 2 a → + 0 ⇒ 4 a → 2 + b → 2 + 4 a → · b → ⇒ 4 + 1 + 0 ⇒ 5