26. r, s, and t are three distinct lines in a plane, which of the following must be true? I. If r and s are parallel to t, then r is parallel to s. II. If r and s intersect t, then r intersects s. III. If r and s are parallel and s intersects t, then r intersects t. (A) I only (B) III only (C) I and III only (D) II and III only (E) I, II, and III

26. r, s, and t are three distinct lines in a plane, which of the following must be true? I. If r and s are parallel to t, then r is parallel to s. II. If r and s intersect t, then r intersects s. III. If r and s are parallel and s intersects t, then r intersects t. (A) I only (B) III only (C) I and III only (D) II and III only (E) I, II, and III

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 13AEXP

See similar textbooks

Similar questions

Prove the converse to theorem 2.6.2 let l and m be two lines. If there exists a unique point P such that P lies on both l and m, then l and m are distinct and nonparallel.
7. The three planes x + y + z = 0, x + 2y + 2z = 1, and 2x − y + mz = n intersect in a line. Determine the values of m and n for which this is true.
with the guldin's proposition 1 get the contents of the rotating object that occurs if the land bounded by y = 6-3x-x ^ 2 and x + y-3 = 0, is rotated on the line y = 3-x
Prove theorem 2.6.4. If P is any point, then there are at least two distict lines l and m such that P lies on both l and m
Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through P and Q is given by det(A) = 0, where
Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.
Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line I with symmetric equations 16 − x = y − 18 = z + 11. - Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. - Determine if the vector KM and the line l are parallel.
Determine α so that the lines r X = (1,0,2) + λ (2, 1, 3) and s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.
If a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2 . (without using analytical geometry)
4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the equation x-1/2 = y-2/3 = z-4/5. Find the distance of the point (1, 1, 1) to the plane α
What are the coordinates of the vertices of△A′B′C′after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?
c. Draw a figure when the plane intersects only one cone and parallel to any generator forming an unbounded curve d. Draw a figure when the plane (not necessarily vertical) intersects both cones forming two unbounded curves (each called a branch).