Explain why or why not Determine whether the following statements 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 3 intersect. c. The plane x + y + z = 0 and the line x = t, y = t, 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 ℝ 3 determine a unique plane. g. The vector ⟨−1, −5, 7⟩ is perpendicular to both the line x = 1 + 5 t , y = 3 − t, z = 1 and the line x = 7 t , y = 3, z = 3 + t.
Explain why or why not Determine whether the following statements 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 3 intersect. c. The plane x + y + z = 0 and the line x = t, y = t, 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 ℝ 3 determine a unique plane. g. The vector ⟨−1, −5, 7⟩ is perpendicular to both the line x = 1 + 5 t , y = 3 − t, z = 1 and the line x = 7 t , y = 3, z = 3 + t.
Explain why or why not Determine whether the following statements 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 ℝ3 intersect.
c. The plane x + y + z = 0 and the line x = t, y = t, 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 − t, z = 1 and the line x= 7t, y = 3, z = 3 + t.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
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Introduction to Statistics..What are they? And, How Do I Know Which One to Choose?; Author: The Doctoral Journey;https://www.youtube.com/watch?v=HpyRybBEDQ0;License: Standard YouTube License, CC-BY