10. Four points that are coplanar11. Three lines that intersect at one point12. A line and a plane that intersect at one point

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Answered: 10. Four points that are coplanar 11.…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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1. Find the plane which contains the point M (4,5,0) and the line ²+³ = - = -².
3. Consider the line [x,y,z] = [3,-2,3]+1[-1,2,-3]. Find the intersection points between this line and the co-ordinate axes. is.
1. Find the volume of the parallelepiped having edges or else shore that A, B, C, and D lie on a plane they lie on a find its equations. AB, AC, and AD, or on a line. If plane, find its equation; if they lie on a line. A(2,-1,3), B = (-1,2,2), (= (1,0,1), D= (4,1-1) 2. Compute (uxv) xw directly U=2; 13j-k, V = i-as +k, w = ~ i tj tak 3. Find the equation of the line through the given point and perpendicular to the given line and intersecting it. (2,-1,3); X11 = 1-2 = 2+1 3 4. Express (txu) x (vxw) in terms of v and w t = i tj - 2k, u = 3; -j tak, v = zitaj -k, w= -itj tak
II. #1-5 Write True if the statement is True, and False if not.
9. Determine the Cartesian equation of the plane that contains the intersecting lines: -2 y 2+3 x-2 1₁:X-2 = y_z+3 = and 1₂: = 2 3 -3 4 2
18. Which point does not lie on the same plane as the points P(1,5,6), Q(-2,-3,4), and R(-1,3,2)? a. S(0,-1,8) C. c. S(1,-3,2) S(4,13,8) b. S(0,4,4) d. 19. Determine which line is perpendicular to the line 2x-3y + 17 = 0. a. r = (1,2) + s (3,2), s € R C. r = s(3,2), SER s b. 7 = (1,7) + s(2,-3), s € R d. r = (2,-3) + s(3,-2), SER
State the postulate that can used to show that statement is true.
10. Line in the xy-plane contains points from each of the Quadrants I, III, and IV, but no points from Quadrant II. Which of the following must be true? A) The slope of line B) The slope of line C) The slope of line D) The slope of line is zero. is undefined. is positive. is negative.

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10. Four points that are coplanar 11. Three lines that intersect at one point 12. A line and a plane that intersect at one point