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Chapter 10: Q. 11 (page 788)

What point is symmetric about the origin to the point \((5, −6, 7)\)?

Short Answer

Expert verified

The symmetric point of \((5, -6, 7)\) about the origin is \((-5, 6, -7)\)

Step by step solution

01

Step 1. Given Information

The given point is \((5, -6, 7)\).

Here, \(x\) and \(z\) are positive and the \(y\) coordinate is negative. Thus, the above point lies in the third octant.

02

Step 2. Finding the symmetric point

As the given point lies in the third octant, its symmetric point will lie in the sixth octant where both the x and z coordinates are negative and the y coordinate is positive.

Therefore, the symmetric point of \((5,-6,7)\) about the origin \((0,0)\) is \((-5,6,-7)\).

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Most popular questions from this chapter

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.

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

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

P(1,6),Q(0,−3),R(−5,4)

(Hint: Think of the xy-plane as part of ℝ3.)

Find PQ⇀

P=5,-3,Q=3,-6

Find PQ→

P=1,-2,5,Q=1,-7,-2

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.

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

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

P(3,1,8),Q(0,6,−1),R(−3,5,−3)

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

u=2,0,-5,v=-3,7,-1
See all solutions

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