The intersection of the two planes given by the vector equations()-r.= 42and6.r.-2| 4isO a. a planeO b. a line passing through the point (1,1,1)O c. the line l1x = y-1=zO d. a pointe. the empty set3.

We have to find the intersection of the planes r·3-12=4 and r·6-24=9. Let the vector r=xyz. The…

Answered: The intersection of the two planes…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which equation describes the sum of the two vectors plotted below? O A. r=-X + 3y B. r y O C. r=x l ý D.r 2x 1 y SUBMIT + PREVIOUS
H H Select all of the vectors that are in the span of {u₁, u₂}. (Check every statement that is correct.) Let u₁ = A. The vector 9 B. The vector D. The vector and u₂ [] OC. All vectors in R² are in the span. E. The vector F. The vector 8 -5 -5 is in the span. -51 is in the span. is in the span. is in the span. +9 [-] is in the span. G. We cannot tell which vectors are in the span.
pls help with these thanks. 1. a) Determine a direction vector of the line of intersection of the two planes 6x - 2y + 8z = 14 and 15x - 5y + 20z = 28. If there is not a single line of intersection, classify the system. Question a) options: [-7, 3, -5] [4, -6, 1] [-6, -5,2] [1, -7, -4] parallel and distinct coincident b) Solve the following system, if possible. π1: 3x - 2y + 5z = 1 π2: 5x + y - 3z = -4 π3: 6x - 17y + 44z = 31 Find either the point of intersection or the direction vector of the line of intersection or state the system is inconsistent. Question b) options: [1, -5, –3] [-3, 5,-1] [8, 4, 1] [-4, -7, 5] inconsistent
For each vector, find the angle that the vector makes with the x-axis. Round your answers to the nearest 0.1◦.10a. ⟨5, 2⟩, 10b. ⟨−6, 1⟩, 10c. ⟨−3, −4⟩, 10d. ⟨2, −1⟩,10e. ⟨3, 0⟩, 10f. ⟨0, 4⟩, 10g. ⟨−2, 0⟩, 10h. ⟨0, −8⟩.
28. How are lines expressed as vectors? a. Express 2 points along the line as vectors from the origin, then dot product the vectors b. Express 2 points along the line as vectors from the origin, then cross product the vectors c. Express 2 points along the line as vectors from the origin, then subtract the vectors d. Express 2 points along the line as vectors from the origin, then add the vectors
The intersection of the two planes given by the vector equations -3 r. {} -2 2 and r. is 9 -4 = -2 4 a. a line passing through the point (1,1,1) b. a plane c. the empty set d. the line 11x=y-1 =z e. a point
33. Find the direction and magnitude of the vectors. a. A = (5.0 m) x + (-2.0 m) y, →>> →>> b. B = (-2.0m) x + (5.0 m) y, and (c) A + B. → a. A = (22 m) x + (-14 m) y, b. B = (2.5 m) x + (13 m) ỹ, and (c) A + B. • For the vectors given in Problem 34, express (a) A – B and (b) B – A in unit vector notation.
a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

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The intersection of the two planes given by the vector equations 3 r. -1 = 4 and r. 4. is O a. a plane O b. a line passing through the point (1,1,1) O c. the line llx = y-1=z O d. a point e. the empty set 2. 2.