Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The line r = (3, -1,4) + t(6, –2, 8) passes through the origin. b. Any two nonparallel lines in R° intersect. c. The plane x + y + z = 0 and the line x = 1, y = 1, z = t are parallel. d. The vector equations r = (1, 2, 3) + t(1, 1, 1) and R = (1, 2, 3) + t(-2, –2, –2) describe the same line. e. The equations x + y – z = 1 and -x – y + z = 1 describe the same plane. f. Any two distinct lines in R³ determine a unique plane. g. The vector (-1, –5, 7) is perpendicular to both the line x = 1 + 5t, y = 3 – 1, z = 1 and the line x = 7t, y = 3, z = 3 + t. %3D

Q: Determine the accuracy of the statements given below. X = 1- 2t I: x+ 2y+ 2z = 3 plane and y = 2+ 3t…

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Q: mal ni 080 23. 2291 D 3x bni For hey A %23 B bag ABC is a straight line.

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Q: Find the point (if it exists) at which the following plane and line intersect. y=-7; r(t) = (3t+1,…

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Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: show. that theAine in.which.the planes.X+.2y-22=-5 nod5X-2y.z=.0...jntersec.is..pavalle.to.theine.…

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Q: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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Q: Calculate the requaested distance. 1. The distance from the point S(7, -2, -5) to the plane 2x + 2y…

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Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z][-1, -9,16]++[3, 3,…

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Q: 8. For each pair of lines and m below determine whether the lines intersect, are parallel or…

A: Please see the below pictures for detailed solution.

Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Which of the following  points in the standard (x, y) coordinate plane is furthest from the origin

Q: Consider the following: a. Write an equation of a plane in Cartesian form that contains the point…

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A: (Note: We are entitled to solve only one question at a time) To Find: The lines containing the point…

Q: Please answer one question asap. Thank you!!! 26. Find the intercepts of the plane [x,y,z] = [5,4,3]…

A: To find the intercepts of the plane given by the equation [x,y,z]=[5,4,3]+s[1,0,1]+t[−1,−4,−2], we…