In Exercises 15-18, let R² have the Euclidean inner product. a. Find the orthogonal projection of u onto the line spanned by the vector v. b. Find the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. 15. и %3D (-1, 6); v %3D = () 16. u = (2, 3); v = 12 13' 13 5' 5
In Exercises 15-18, let R² have the Euclidean inner product. a. Find the orthogonal projection of u onto the line spanned by the vector v. b. Find the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. 15. и %3D (-1, 6); v %3D = () 16. u = (2, 3); v = 12 13' 13 5' 5
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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![In Exercises 15–18, let R² have the Euclidean inner product.
a. Find the orthogonal projection of u onto the line spanned by
the vector v.
b. Find the component of u orthogonal to the line spanned by
the vector v, and confirm that this component is orthogonal
to the line.
15. и %3D (-1, 6); v %3D
) 16. u = (2, 3); v= ()
16. и 3D (2, 3); v 3
13' 13
17. u = (2, 3); v= (1,1)
18. и %3D (3, —1); v%3D (3,4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F365ed42d-254e-4fb1-901e-51705083fdfa%2Fbe8945e1-f8d2-45a2-8385-52783e3954fa%2Fgiqjqsw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 15–18, let R² have the Euclidean inner product.
a. Find the orthogonal projection of u onto the line spanned by
the vector v.
b. Find the component of u orthogonal to the line spanned by
the vector v, and confirm that this component is orthogonal
to the line.
15. и %3D (-1, 6); v %3D
) 16. u = (2, 3); v= ()
16. и 3D (2, 3); v 3
13' 13
17. u = (2, 3); v= (1,1)
18. и %3D (3, —1); v%3D (3,4)
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