1. Still considering the same vectors a := h1, 3i, b := h2, −2i, c := h4, 0i, and d := h−3,−1i, what are the following? 1.a • b 2.a • d 3.c • c 2. 3. Suppose that the Manhattan distance between...

1. Still considering the same vectors a := h1, 3i, b := h2, −2i, c := h4, 0i, and d := h−3,−1i, what are the following?

1.a • b

2.a • d

3.c • c

2.

3. Suppose that the Manhattan distance between two vectors x, y ∈ R2

is 1. Justify your answers:

1. What’s the largest possible Euclidean distance between x and y?

2. What’s the smallest possible Euclidean distance between x and y?

3. What’s the smallest possible Euclidean distance between x and y if x, y ∈ Rn

(not just n = 2)?