Answer to Question #113756 in Analytic Geometry for DUMISANE CHAUKE

Question

Which of the following statements is/are true? Explain why the false one is false. A. If u = (u1; u2) with ui not eqaual to 0 for some 1 <= i <= 2; then the unit vector in the direction of u is 1/sqrt( u1^2 +u2^2 )(u1; u2) : (2) B. u = (1; 2; 3) is the unit vector in the direction of u: (

Answer 1

A) By the definition, unit vector: u' = u / ||u|| = (u₁, u₂) / (u₁² + u₂²)^1/2. True.

B) u' = u / ||u|| = (u₁, u₂, u₃) / (u₁² + u₂² + u₃²)^1/2 = (1, 2, 3) / (1² + 2² + 3²)^1/2 = (1/(14)^1/2)(1, 2, 3).