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

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