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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 point that is symmetric to the point \((−1, 3, 6)\) with

respect to the XY-plane is \((-1,3,-6)\).

Step by step solution

01

Step 1. Given Information

The given point is \((−1, 3, 6)\)

Here, the x coordinate is positive, and both the y and z coordinates are negative. Thus, the given point lies in the fifth octant.

02

Step 2. Finding the symmetric point.

As the given point lies in the fifth octant, its symmetric point about XY-plane lies in the sixth octant where both the x and z coordinates are negative and the y-coordinate is positive.

Therefore, the point that is symmetric to the point \((−1, 3, 6)\) with

respect to the XY-plane is \((-1,3,-6)\)

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Most popular questions from this chapter

Prove the first part of Theorem 1.31(a): If k>0, then limx→∞xk=∞. (Hint: Given M>0, choose N=M1/k. Then show that for x>N it must follow that xk>M.)

Find a vector of length 3 that points in the direction opposite to1,-2,3.

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

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P(4,3,−2),Q(0,0,3),R(−1,3,6)

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

localid="1649405204459" role="math" (u×v)·wandu·(v×w)

Find the norm of the vector.v=0,0,6
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