Let a → = cos ⁡ θ i ^ - s i n θ j ^ ,   b → = sin ⁡ θ i ^ + cos ⁡ θ j ^ ,   c → = k ^ and r → = 7 ı ^ + j ^ + 10 k ^ . If r → = x a → + y b → + z c → , then the value of x 2 + y 2 z is equal to

Step-by-step solution

r → = x cos ⁡ θ + y sin ⁡ θ i ^ + - x sin ⁡ θ + y cos ⁡ θ j ^ + z k ^ ∵ r → = 7 ı ^ + j ^ + 10 k ^ on comparison x cos ⁡ θ + y sin ⁡ θ = 7 … … . i - x sin ⁡ θ + y cos ⁡ θ = 1 … … . i i z = 10 Squaring and adding equation i and i i x 2 + y 2 = 7 2 + 1 2 = 50 ⇒ x 2 + y 2 z = 50 10 = 5