Question: Problem 1: Thinking about vectors, angles, and dot products Consider the plot below with 3 data points on the x - y plane. Let's define

Problem 1: Thinking about vectors, angles, and dot products Consider the plot below with 3 data points on the x - y plane. Let's define 3 vectors u, v, and w : u = OA V = OB w = OC , where point 0 = The origin (0,0) (a) Find the vectors u , 1 , and w that specify the positions of the data points A, B, and C with respect to the origin (b) Calculate the dot product u . B and angle 0, between the 2 vectors (c) Calculate the dot product B . w and angle 02 between the 2 vectors (d) Calculate the dot product w . u and angle 03 between the 2 vectors (e) Calculate 01 + 82 + 03 (f) Using the plot, explain why your answer to (e) makes geometrical sense. Data points ! A A N O y-values O B -2 C -5 . Raw data points 5 -3 -2 0 2 5 4 -1 3 x-values

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