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Chapter 10: Q 27 (page 789)

Find the distance between the points(0,0,...,0)and(1,1,...,1)inn-space

Short Answer

Expert verified

The required distance isn

Step by step solution

01

Given information

The given points are(0,0,...,0)and(1,1,...,1)inn-space

02

Finding the distance

The distance may be found as per formula as under:

(1-0)2+(1-0)2+(1-0)2+...ntimes

Simplify:

1+1+1+...ntimes

Simplify further:

n

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Most popular questions from this chapter

If u and v are vectors in ℝ3 such that u×v=v×u, what can we conclude about u and v?

A function f that satisfies the hypotheses of Rolle’s Theorem on [−2, 2] and for which there are exactly three values c ∈ (−2, 2) that satisfy the conclusion of the theorem .

Fill in the blanks to complete each of the following theorem statements:

For ε>0,f(x)∈(L-ε,L+ε)if and only if<ε.

In Exercises 30–35 compute the indicated quantities when

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In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

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(c) The area of the triangle determined by the points.

P(4,3,−2),Q(0,0,3),R(−1,3,6)
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