Question: Please help me with the e, f, g Question 3. Vector and geometry (15 marks) Consider the vectors u=(1,2,1),v=(2,4,1),w=(1,1,3), and let U,V,W be the corresponding

Please help me with the e, f, g

Please help me with the e, f, g Question 3. Vector and geometry (15 marks) Consider the vectors u=(1,2,1),v=(2,4,1),w=(1,1,3), and let U,V,W be the

Question 3. Vector and geometry (15 marks) Consider the vectors u=(1,2,1),v=(2,4,1),w=(1,1,3), and let U,V,W be the corresponding points in R3, respectively. (e) Calculate the vector projection of u onto v. [1 mark] (f) Use Mathematica to find the area of the parallelogram spanned by v and w. [2 marks] 2 (g) Use Mathematica to find the volume of the parallelopiped spanned by u,v and w, and the volume of the tetrahedron spanned by u,v and w. [2 marks] Question 3. Vector and geometry (15 marks) Consider the vectors u=(1,2,1),v=(2,4,1),w=(1,1,3), and let U,V,W be the corresponding points in R3, respectively. (e) Calculate the vector projection of u onto v. [1 mark] (f) Use Mathematica to find the area of the parallelogram spanned by v and w. [2 marks] 2 (g) Use Mathematica to find the volume of the parallelopiped spanned by u,v and w, and the volume of the tetrahedron spanned by u,v and w. [2 marks]

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