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Chapter 10: Q. 12 (page 788)

What point is symmetric to the point (−1,3,6) with respect to the xy-plane?

Short Answer

Expert verified

The symmetric xy-plane point to the point(-1,3,6)is (-1,3,-6).

Step by step solution

01

Introduction.

It is symmetrical if the yand xvalues of a arithmetic formula can be swapped the line y=x.

02

Given Information.

Consider the following statement:

(-1,3,6)

The goal is to find the point on the xy-plane that is symmetric to this point.

03

Explanation.

Since the yand zcoordinates are both positive and the xcoordinate is negative, the point (-1,3,6)is in the fifth octant.

The point symmetric about the xy-plane to this point will be below the xy-plane with a negative zcoordinate, which is the sixth octant.

In the sixth octant, the xand ycoordinates are both negative, while the ycoordinate is positive.

As an outcome, the point symmetric to the point (-1,3,6)about xy-plane is (-1,3,-6).

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Most popular questions from this chapter

In Exercises 37–42, find v and find the unit vector in the direction of v.

v=1,1,1

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649603943715" u=3,6,11andv=1,-2,3

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v×wandw×v

In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

role="math" localid="1649693816584" u=3,1,-2,v=-6,-2,4

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is k=1.

(b) True or False: ∑k=0n 1k+1+∑k=1n k2is equal to ∑k=0n k3+k2+1k+1.

(c) True or False: ∑k=1n 1k+1+∑k=0n k2is equal to ∑k=1n k3+k2+1k+1 .

(d) True or False: ∑k=1n 1k+1∑k=1n k2 is equal to ∑k=1n k2k+1.

(e) True or False: ∑k=0m k+∑k=mn kis equal to∑k=0n k.

(f) True or False: ∑k=0n ak=−a0−an+∑k=1n−1 ak.

(g) True or False: ∑k=110 ak2=∑k=110 ak2.

(h) True or False: ∑k=1n ex2=exex+12ex+16.
See all solutions

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