Distance between parallel hyperplanes Consider two hyperplan

Distance between parallel hyperplanes. Consider two hyperplanes. H_1 = {x epsilon R^n|a^T x = b}, H_2 = {y epsilon R^n|a^T y = c}, where a is a nonzero n-vector, and b and c are scalars. The hyperplanes are parallel because they have the same coefficient vectors a. The distance between the hyperplanes is defined as d = min ||x - y|| x epsilon H_1 y epsilon H_2 Which of the following three expressions for d is correct? Explain your answer. d = |b - c| d = |b - c|/||a|| d = |b - c|/||a||^2.

option (b)

proof let

Therefore the intersection point is x2=x1+a(bbcccc)/aTa. The distance between these two points is the distance between the hyperplanes:

a T (x 1 + a t) = c t = (c b c a T x 1) / a T a = (b c) / a T a

Therefore the intersection point is x2=x1+a(bbcccc)/aTa. The distance between these two points is the distance between the hyperplanes:

x 1 x 2 = |b c cc | a T a a = | b c cc | a

$Distance between parallel hyperplanes. Consider two hyperplanes. H_1 = {x epsilon R^n|a^T x = b}, H_2 = {y epsilon R^n|a^T y = c}, where a is a nonzero n-vecto$

Distance between parallel hyperplanes Consider two hyperplan

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