If θ is the angle between the vectors 4 i ^ - k ^ and i ^ + j ^ + k ^ , then sin θ + cos θ equals to

Step-by-step solution

Let a → = i ^ + j ^ + k ^ b → = 4 i ^ - k ^ Then, a → = 1 2 + 1 2 + 1 2 = 3 b → = 4 2 + 0 2 + - 4 2 = 4 2 Now, cos θ = a → · b → a → b → ⇒ cos θ = i ^ + j ^ + k ^ · 4 i ^ - 4 k ^ a → b → ⇒ cos θ = 4 - 4 a → b → = 0 Hence, sin θ = 1 - cos 2 θ = 1 Therefore, sin θ + cos θ = 1