Let an ant starts from the origin O and travels 2 units on negative x -axis, 3 units on positive y -axis and travels 3 units on negative z -axis to reach at point A . If a → = i ^ - 3 j ^ + 2 k ^ and b → be such that the resultant of a → and b → is 3 i ^ - 4 j ^ + k ^ , then O A → × a → × b → 2 is equal to

Step-by-step solution

O A → = - 2 i ^ + 3 j ^ - 3 k ^ , a → = i ^ - 3 j ^ + 2 k ^ a → + b → = 3 i ^ - 4 j ^ + k ^ (given) ⇒ b → = 2 i ^ - j ^ - k ^ O A → × a → × b → = O A → ⋅ b → a → - O A → ⋅ a → b → = - 4 a → + 17 b → = - 4 i ^ - 3 j ^ + 2 k ^ + 17 2 i ^ - j ^ - k ^ = 30 i ^ - 5 j ^ - 25 k ^ O A → × a → × b → 2 = 900 + 25 + 625 = 1550