@Let P(1,2,3) and Q(2,3,1) be two points in R 3 . The aim of this exercise is to

ID: 3103064 • Letter: #

Question

@Let P(1,2,3) and Q(2,3,1) be two points in R3. The aim of this exercise is to find the coordinates of the points R(a,b,c) R3 such that

(b)What is the nature of the set of values of a,b,c satisfying the condition found in (a)?

(c)State the Pythagorean Theorem in n-Space.

(d)Compute the norms of the vectors PQ and PR.

(e) Using the Pythagorean Theorem, find an equation that must be satisfied by the coordinates a,b,c of R. [hint: this equation is not linear.]

(f)What is the nature of the set of values of a,b,c satisfying the conditions found in (e)? [you can use a geometrical argument.]

(g)Deduce a system characterizing the set of points satisfying (*).

(h)What is the nature of the set of values of a,b,c satisfying the conditions found in (g)?

p (1,2,3)&q(2,3,1)

=(2,3,1)

=(4,6,2)

=(6,9,3)

coordinates of the points is a(2,3,1), b(4,6,2),c(6,9,3)

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