Which of these planes pass through the origin?Зх — 5у + 2z 305х — 3 3D 04х + у %3D 0-4x – 5y + z = 28x + 7y = 2zбх — 5у %3D 1

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Answered: Which of these planes pass through the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(part 1 of 4) Suppose you start at the origin in 3-space, move along the x-axis a distance of 2 units in the positive direction, and then move down- ward a distance of 3 units. What are the coordinates of your position? 1. (2,0, -3) 2. (2, -3,0) 3. (2,0,3) 4. (0, 2, -3) 5. (0, -3,2) (part 2 of 4) Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the xz-plane? 1. R(-5, 8, 1) 2. P(6, 9, -3) 3. Q(8, -2, -8) (part 3 of 4) A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (1,0,0), (0,3,0), (0,0,2). Find the length of the diagonal of the box. 1. length 14 2. length 3. length 4. length 5. length 6. length = = = = √22 √14 √19 19 22 (part 4 of 4) What are the coordinates of the projection of the point Q(-4, 5, 3) onto the zx-plane? 1. (-4, 0, 3) 2. (-4, -5, 3) (4, 5, 3) 3. 4. (-4, 5, 0) 5. (-4, 5, -3) 6. (0,5, 3)
Find an equation of the plane passing through the given points. (1, 0, 19), (4, 2, 14), (2, -1, 19)
8. A theme that will later unfold concerns the use of coordinate systems. We can identify the point (x, y) with the tip of the vector drawn emanating from the origin. We can then think of the usual Cartesian coordinate system in terms of linear combinations of the vectors ej = e2 = V2 V1 (2, –3) 42,–3} Figure 2.1.8. The usual Cartesian coordinate system, defined by the vectors ej and e2, is shown on the left along with the representation of the point (2, -3). The right shows a nonstandard coordinate system defined by vectors v1 and v2. The point (2, -3) is identified with the vector — 2е1 — Зе2. If we have vectors v1 = ,v2 = we may define a new coordinate system, such that a point {x, y} will correspond to the vector xv1 + yv2. For instance, the point {2, –3} is shown on the right side of Figure 2.1.8 Write the point {2, –3} in standard coordinates; that is, find r and y such that а. (», у) 3 {2, —3}. b. Write the point (2, –3) in the new coordinate system; that is, find a and b such…
Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?
Let u1 = (4, -2, 1), u2 = (6,3,2) , u3 = (-2,-1,3) find the linear combination v= u1 - 3u2+ 4u3
Find an equation of the plane passing through the given points. (5, 2, 13), (3, -3, 20), (1, -1, 20)
4 - Investigate Interaction of Two Planes Plot the following and their normal vectors. 2x-2y + 2z = 15 3x - 3y + 3z = -13 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. State the normal of both planes. Include the plot below and feel free to provide a link.
Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.
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Which of these planes pass through the origin? Зх — 5у+ 2z 30 5х — 3 %3D 0 = 4х + у %3D 0 — 4х — 5у + z %3 2 8х + 7у 3D 2z О бх — 5у %3D 1 6x