Module 1: Part 2 Fundamental Concepts: Vectors 1. Consider a vector A such that A 6 î 2 ĵ k̂ . How would you write the vector in a coordinate system where the unit vectors are û , v̂ , and ŵ where û 2 1 1 î ĵ k̂ 6 6 6 v̂ -1 1 1 î ĵ k̂ 3 3 3 ŵ 0 î 3 3 ĵ k̂ 18 18 Hint: Write the vector in the form A au û av v̂ awŵ Stop – Prepare To Outbrief 2. For spherical coordinates, A. How would you write the position vector of a particle in spherical coordinates? Draw a picture of your vector, coordinate system, and unit vectors). B. Write the ρ̂ , ̂ , and θ̂ in terms of î , ˆj , and k̂ . C. The scalar product of two vectors A and B in Cartesian coordinates is given by A B A x B x A y B y A z Bz . Is the scalar product in spherical coordinates A B Aρ Bρ A B A B ? θ θ Explain your reasoning or provide a mathematical proof. Stop – Prepare To Outbrief 3. If the position vector of a particle is given by 2 r t 2t î 3 e 2t ĵ 2Sin(5t) k̂ A. Find the initial velocity of the particle. A. Find the initial acceleration of the particle. Stop – Prepare To Outbrief