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Chapter 10: Q 13. (page 845)

Explain why any two skew lines lie on a unique pair of parallel planes.

Short Answer

Expert verified

Any point from line L1 along with N and any point from line L2 along with N determine the unique pair of parallel planes.

Step by step solution

01

Given information

The two skew lines L1 and L2

02

Calculation

Take a look at the two skew lines L1and L2

The goal is to explain why two skew lines are parallel to each other on a single set of parallel lines.

Use the skew line definition to demonstrate the effect.

If the lines do not intersect or are not parallel, they are skewed.

The lines L1and L2are skew. It means that lines L1and L2neither intersect nor are parallel. Assume that d1and d2be the direction vectors of the skew lines L1 and L2

03

Calculation

Since, the lines are skew, therefore,

N=d1×d2≠0

Therefore, any point from line L1 along with N and any point from line L2 along with N determine the unique pair of parallel planes.

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Most popular questions from this chapter

Find a vector in the direction of -1,2,3with magnitude 3.

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)

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

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

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

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

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