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Homework Statement
In Rn, define A = (0, 0, ..., 0) and B = (1, -1, ..., (-1)n-1)
Find (1) the parametric form of the line through A and B, (2) as an intersection of (n-1) hyperplanes, and (3) the hyperplane crossing the origin, normal to AB.
Homework Equations
AB = ((1-0),(-1-0),...,(-1)n-1-0) = (1,-1,...,(-1)n-1)
The Attempt at a Solution
A = (0,0,...,0)
B = (1,-1,...,(-1)n-1)
AB = ((1-0),(-1-0),...,(-1)n-1-0)
AB = (1,-1,(-1)n-1)
Parametric form:
[x1 x2 ... xn] = [0 0 ... 0] + s[1 -1 ... (-1)n-1]
Intersection with plane (I'm really lost here):
a1(x1)+a2(x2)+...+an(xn)
a1(0+1s)+a2(0-1s)+...+an(0+(-1)n-1s)
a1(s)-a2(s)+...+an((-1)n-1s)
Hyperplane crossing the origin, normal to AB:
Would this just be the nAB x nplane?
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