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Chapter 10: Q. 12 (page 788)

What point is symmetric to the point (鈭�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 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

Find the volume of the parallelepiped determined by the vectors u, v, and w.

Read the section and make your own summary of the material.

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

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

(b) Two unit vectors perpendicular to the plane determined by the points.

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

P(4,鈭�2),Q(鈭�2,0),R(1,鈭�5)

(Hint: Think of the xy-plane as part of 鈩�3.)

In Exercises 30鈥�35 compute the indicated quantities when

u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

u脳vandv脳u

Find u+vand u-v. Also sketchu,v,u+vand u-v.

role="math" localid="1649578020551" u=3,-4andv=-1,5
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