a = 3 b = 5 c = 4 d = 6 e = 2 Human Genetics: The angle between two n-dimensiona

Question

a = 3

b = 5

c = 4

d = 6

e = 2

Human Genetics: The angle between two n-dimensional vectors can be found using the dot product. Assume that two populations are genetically close if the angle of their alleles' relative frequencies is small. Let P1, P2, P3, P4 be four different human populations with the following respective vector representation in 4-dimensional space of the relative frequencies of their alleles. Part a) Is the population P3 closer to P4 or P2? Part b) Is P3 closer to a half of Pl, half of P2 than to P2 alone? Part c) Among all possible populations that are a mix of P1 and P2, find the mix that is closest to P3. Note: For Problem 1 Part c, use x as the percent of P1 and (1-x) as the percent of P2 and find the minimum of the angle by graphing with respect to x, not by derivatives. Use the same process for Problem 2 below.

Explanation / Answer

i think that a=3

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