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In Exercises 19–22, let R³ have the Euclidean inner product. a. Find the orthogonal projection of u onto the plane spanned by the vectors V¡ and v2. b. Find the component of u orthogonal to the plane spanned by the vectors v, and v,, and confirm that this component is orthogonal to the plane. -i), v. 2 1 19. u = (4, 2,1); v, = 3' 3 3' 3' 3 = 'a (- (우·우 (ㅎ) 20. u = (3, –1,2); vị 21. u = (1,0, 3); v, = (1, –2, 1), v, = (2,1,0) 22. u = (1,0, 2); vị = (3,1,2), v2 = (-1,1,1)

In Exercises 19–22, let R³ have the Euclidean inner product. a. Find the orthogonal projection of u onto the plane spanned by the vectors V¡ and v2. b. Find the component of u orthogonal to the plane spanned by the vectors v, and v,, and confirm that this component is orthogonal to the plane. -i), v. 2 1 19. u = (4, 2,1); v, = 3' 3 3' 3' 3 = 'a (- (우·우 (ㅎ) 20. u = (3, –1,2); vị 21. u = (1,0, 3); v, = (1, –2, 1), v, = (2,1,0) 22. u = (1,0, 2); vị = (3,1,2), v2 = (-1,1,1)

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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In Exercises 19–22, let R³ have the Euclidean inner product. a. Find the orthogonal projection of u onto the plane spanned by the vectors v¡ and v2. b. Find the component of u orthogonal to the plane spanned by the vectors vị and v2, and confirm that this component is orthogonal to the plane. = (3. §.-}). v. = (3, } ) v; = (#) 19. u = (4, 2,1); vị 3' 3' 3 20. u = (3, –1,2); vị = (- 21. u = (1,0, 3); v = (1, –2, 1), v2 = (2,1,0) 22. u = (1,0, 2); v, = (3,1,2), v, = (-1,1,1)
Transcribed Image Text:In Exercises 19–22, let R³ have the Euclidean inner product. a. Find the orthogonal projection of u onto the plane spanned by the vectors v¡ and v2. b. Find the component of u orthogonal to the plane spanned by the vectors vị and v2, and confirm that this component is orthogonal to the plane. = (3. §.-}). v. = (3, } ) v; = (#) 19. u = (4, 2,1); vị 3' 3' 3 20. u = (3, –1,2); vị = (- 21. u = (1,0, 3); v = (1, –2, 1), v2 = (2,1,0) 22. u = (1,0, 2); v, = (3,1,2), v, = (-1,1,1)
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