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CHAPTER 9. MULTIVARIABLE AND VECTOR FUNCTIONS Activity 9.4.4 Suppose u = (3, 5, -1) and v= (2, -2, 1). a. Find two unit vectors orthogonal to both u and v. b. Find the volume of the parallelepiped formed by the vectors u, v, and w = (3,3, 1). 25 c. Find a vector orthogonal to the plane containing the points (0, 1, 2), (4, 1,0), and (-2, 2, 2). d. Given the vectors u and v shown below in Figure 9.4.4, sketch the cross products u x v and v x u. y Y u Figure 9.4.4 Vectors u and v e. Do the vectors a = (1,3,-2),b= (2, 1,-4), and c = (0, 1, 0) in standard position lie in the same plane? Use the concepts from this section to explain.

CHAPTER 9. MULTIVARIABLE AND VECTOR FUNCTIONS Activity 9.4.4 Suppose u = (3, 5, -1) and v= (2, -2, 1). a. Find two unit vectors orthogonal to both u and v. b. Find the volume of the parallelepiped formed by the vectors u, v, and w = (3,3, 1). 25 c. Find a vector orthogonal to the plane containing the points (0, 1, 2), (4, 1,0), and (-2, 2, 2). d. Given the vectors u and v shown below in Figure 9.4.4, sketch the cross products u x v and v x u. y Y u Figure 9.4.4 Vectors u and v e. Do the vectors a = (1,3,-2),b= (2, 1,-4), and c = (0, 1, 0) in standard position lie in the same plane? Use the concepts from this section to explain.

Advanced Engineering Mathematics
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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CHAPTER 9. MULTIVARIABLE AND VECTOR FUNCTIONS Activity 9.4.4 Suppose u = (3, 5, -1) and v = (2, -2, 1). a. Find two unit vectors orthogonal to both u and v. 25 b. Find the volume of the parallelepiped formed by the vectors u, v, and W = (3, 3, 1). c. Find a vector orthogonal to the plane containing the points (0,1,2), (4, 1,0), and (-2, 2, 2). d. Given the vectors u and v shown below in Figure 9.4.4, sketch the cross products u xv and v x u. y Y Figure 9.4.4 Vectors u and v e. Do the vectors a = (1, 3, -2),b= (2, 1,-4), and c = (0, 1, 0) in standard position lie in the same plane? Use the concepts from this section to explain.
Transcribed Image Text:CHAPTER 9. MULTIVARIABLE AND VECTOR FUNCTIONS Activity 9.4.4 Suppose u = (3, 5, -1) and v = (2, -2, 1). a. Find two unit vectors orthogonal to both u and v. 25 b. Find the volume of the parallelepiped formed by the vectors u, v, and W = (3, 3, 1). c. Find a vector orthogonal to the plane containing the points (0,1,2), (4, 1,0), and (-2, 2, 2). d. Given the vectors u and v shown below in Figure 9.4.4, sketch the cross products u xv and v x u. y Y Figure 9.4.4 Vectors u and v e. Do the vectors a = (1, 3, -2),b= (2, 1,-4), and c = (0, 1, 0) in standard position lie in the same plane? Use the concepts from this section to explain.
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