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ME 5613: Advanced Fluid Mechanics 2016 Tensor Algebra and Kinematics Page 1 Homework #2 Due by 6pm, September 18 1.Suppose 𝐴⃗is a vector, 𝜙 is a scalar, and 𝑛̂is a unit vector. Use indicial notation to show (a)∇⃗⃗3.Consider a coordinate system 𝑂𝑥1𝑥2𝑥3with base vectors ?̂?(i=1,2,3). Let a second coordinate system be represented by the base vectors ?̂?′(i=1,2,3) with the following transformation law ?̂3. (a)find ?̂1′in terms of ?̂. (b)find the orthogonal transformation matrix C (c)express the vector 𝑢⃗⃗ = −6?̂1− 3?̂2+ ?̂3in terms of the new set of basis vectors ?̂?′.