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(c) i + 2j, 3i, j + k (e) i,i+j,i+j+k (d) 3j, 21-j,i+5k (f) i+j, i, i+j+k 5. Show that (u xv) x w = (w u)v (w v)u. You may use (9). 6. Show that ux (vxw)+wx (uxv)+vx (wxu) = 0. 7. If A, B, C, are distinct vectors issuing from a common point, show that the vector (A × B) + (B x C) + (CxA) is perpendicular to the plane containing their heads. 8. (Orthogonal separation) Let a given (nonzero) vector u be separated into the sum of two orthogonal vectors, one parallel to a given (nonzero) vector v and the other perpendicular to v (i.e., uupar + Uperp). Show that Upar = (u v)v, Uperp x(uxv), (8.1) 2 where v=v/||v||. 9. Prove the following identities involving quadruple products. HINT: Use (7) and (9). (a) (AxB) (Cx D) = (A C)(B.D) - (A D) (B C) This is Lagrange's identity, of which equation (5.1) of Exer- cise 5 in Section 14.2 is a special case. (b) (AxB) x (C× D) = (A B x D)C - (A. Bx C)D 10. In deriving (9), we introduced the orthonormal basis {1,3, k}, oriented in such a way that v = v₁ỉ, w = w₁i+w₂j,

(c) i + 2j, 3i, j + k (e) i,i+j,i+j+k (d) 3j, 21-j,i+5k (f) i+j, i, i+j+k 5. Show that (u xv) x w = (w u)v (w v)u. You may use (9). 6. Show that ux (vxw)+wx (uxv)+vx (wxu) = 0. 7. If A, B, C, are distinct vectors issuing from a common point, show that the vector (A × B) + (B x C) + (CxA) is perpendicular to the plane containing their heads. 8. (Orthogonal separation) Let a given (nonzero) vector u be separated into the sum of two orthogonal vectors, one parallel to a given (nonzero) vector v and the other perpendicular to v (i.e., uupar + Uperp). Show that Upar = (u v)v, Uperp x(uxv), (8.1) 2 where v=v/||v||. 9. Prove the following identities involving quadruple products. HINT: Use (7) and (9). (a) (AxB) (Cx D) = (A C)(B.D) - (A D) (B C) This is Lagrange's identity, of which equation (5.1) of Exer- cise 5 in Section 14.2 is a special case. (b) (AxB) x (C× D) = (A B x D)C - (A. Bx C)D 10. In deriving (9), we introduced the orthonormal basis {1,3, k}, oriented in such a way that v = v₁ỉ, w = w₁i+w₂j,

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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please solve question 5. and follow the Advanced-Engineering-Mathematics-2nd-Edition-Michael-D-Greenberg book.. give explanation as i am beginner learner

(c) i + 2j, 3i, j + k (e) i,i+j,i+j+k (d) 3j, 21-j,i+5k (f) i+j, i, i+j+k 5. Show that (u xv) x w = (w u)v (w v)u. You may use (9). 6. Show that ux (vxw)+wx (uxv)+vx (wxu) = 0. 7. If A, B, C, are distinct vectors issuing from a common point, show that the vector (A × B) + (B x C) + (CxA) is perpendicular to the plane containing their heads. 8. (Orthogonal separation) Let a given (nonzero) vector u be separated into the sum of two orthogonal vectors, one parallel to a given (nonzero) vector v and the other perpendicular to v (i.e., uupar + Uperp). Show that Upar = (u v)v, Uperp x(uxv), (8.1) 2 where v=v/||v||. 9. Prove the following identities involving quadruple products. HINT: Use (7) and (9). (a) (AxB) (Cx D) = (A C)(B.D) - (A D) (B C) This is Lagrange's identity, of which equation (5.1) of Exer- cise 5 in Section 14.2 is a special case. (b) (AxB) x (C× D) = (A B x D)C - (A. Bx C)D 10. In deriving (9), we introduced the orthonormal basis {1,3, k}, oriented in such a way that v = v₁ỉ, w = w₁i+w₂j,
Transcribed Image Text:(c) i + 2j, 3i, j + k (e) i,i+j,i+j+k (d) 3j, 21-j,i+5k (f) i+j, i, i+j+k 5. Show that (u xv) x w = (w u)v (w v)u. You may use (9). 6. Show that ux (vxw)+wx (uxv)+vx (wxu) = 0. 7. If A, B, C, are distinct vectors issuing from a common point, show that the vector (A × B) + (B x C) + (CxA) is perpendicular to the plane containing their heads. 8. (Orthogonal separation) Let a given (nonzero) vector u be separated into the sum of two orthogonal vectors, one parallel to a given (nonzero) vector v and the other perpendicular to v (i.e., uupar + Uperp). Show that Upar = (u v)v, Uperp x(uxv), (8.1) 2 where v=v/||v||. 9. Prove the following identities involving quadruple products. HINT: Use (7) and (9). (a) (AxB) (Cx D) = (A C)(B.D) - (A D) (B C) This is Lagrange's identity, of which equation (5.1) of Exer- cise 5 in Section 14.2 is a special case. (b) (AxB) x (C× D) = (A B x D)C - (A. Bx C)D 10. In deriving (9), we introduced the orthonormal basis {1,3, k}, oriented in such a way that v = v₁ỉ, w = w₁i+w₂j,
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