Let a → = 3 i ^ + j ^ - k ^ and c → = 2 i ^ - 3 j ^ + 3 k ^ . If b → is a vector such that a → = b → × c → and | b → | 2 = 50 , then 72 - b → + c → 2 is equal to _ _ _ _ _ _ _ _ _ _ .

Step-by-step solution

Given, a → = 3 i ^ + j ^ - k ^ and c → = 2 i ^ - 3 j ^ + 3 k ^ . And b → is a vector such that a → = b → × c → and | b → | 2 = 50 , Now solving, | a → | = | b → × c → | ⇒ 3 2 + 1 2 + 1 2 = | b → | · 2 2 + 3 2 + 3 2 · sin θ ⇒ 11 = 50 · 22 · sin θ ∴ sin θ = 1 10 or cos θ = 99 10 Now solving, 72 - b → + c → 2 we get, 72 - b → + c → 2 = 72 - b → 2 + c &#8594